1. Permanent magnets

Permanent Magnets

What Is a Permanent Magnet?

A permanent magnet is an object that produces its own persistent magnetic field without needing an electric current or another external magnetic field.

Permanent magnets can exert forces on:

• other magnets
• certain magnetic materials
• moving electric charges under suitable conditions

Common permanent magnets include:

• bar magnets
• horseshoe magnets
• refrigerator magnets
• neodymium magnets
• permanent magnets inside motors and speakers

 

 

 

6

Magnetic Poles

Every ordinary permanent magnet has two magnetic poles:

north pole (N)

and:

south pole (S)

The magnetic force is usually strongest near these poles.

For a bar magnet, the poles are located near the two ends.

A freely suspended magnet tends to align approximately with Earth's magnetic field, which is the principle behind a magnetic compass.

Interactions Between Magnetic Poles

Magnetic poles exert forces on one another.

The basic rule is:

like poles repel

unlike poles attract

Therefore:

N facing N → repel

S facing S → repel

N facing S → attract

 

Like Poles Repel

If the north poles of two magnets are brought together, they experience forces pushing them apart.

The same happens when two south poles are brought together.

Therefore:

N ↔ N → repulsion

S ↔ S → repulsion

The magnets do not need to touch for the force to act.

Magnetic forces can act across a distance through a magnetic field.

Unlike Poles Attract

If the north pole of one magnet is brought near the south pole of another magnet, they attract.

Therefore:

N →← S

The force pulls the magnets toward one another.

This attraction also occurs without direct contact because each magnet interacts with the magnetic field produced by the other.

Why Do Magnetic Poles Attract or Repel?

Every magnet produces a magnetic field around itself.

When two magnets are brought together, their magnetic fields interact.

The resulting magnetic forces depend on their relative orientation.

With unlike poles facing:

• the magnetic field pattern connects smoothly between the magnets
• the magnets experience forces toward one another

With like poles facing:

• the field patterns oppose each other in the region between the magnets
• the magnets experience forces away from one another

 

 

 

5

Magnetic Fields

A magnetic field is a region in which a magnetic material, magnet, or moving electric charge can experience a magnetic force.

Magnetic fields are represented using:

magnetic field lines

For a bar magnet, field lines outside the magnet are conventionally drawn:

north → south

Inside the magnet, they continue:

south → north

forming continuous closed loops.

Magnetic Field Around a Bar Magnet

A bar magnet produces a characteristic magnetic field.

 

 

 

6

The field is generally strongest near the poles.

On a field diagram, stronger fields are represented by field lines that are closer together.

Therefore:

closer field lines → stronger magnetic field

Magnetic Field Lines Never End

Unlike the electric field lines associated with isolated electric charges, magnetic field lines form:

continuous closed loops

Outside a bar magnet:

N → S

Inside the magnet:

S → N

This reflects an important property of magnetism: ordinary isolated magnetic north or south poles have not been observed.

Cutting a Magnet

Suppose a bar magnet is cut in half.

You do not obtain:

one isolated north pole

and:

one isolated south pole.

Instead, you obtain:

two smaller magnets

Each has its own:

• north pole
• south pole

 

 

 

5

If the pieces are divided again, each new piece still has both poles.

Magnetic vs Non-Magnetic Materials

Not all materials respond strongly to magnets.

Materials that are strongly attracted to magnets and can often be magnetized are called ferromagnetic materials.

Important examples include:

• iron
• nickel
• cobalt
• many steels
• some alloys

These materials can respond very strongly to magnetic fields.

Ferromagnetic Materials

Ferromagnetism is the strong magnetic behavior found in materials such as iron, nickel, cobalt, and certain alloys.

Inside these materials, groups of atomic magnetic moments can align together.

These aligned regions are called:

magnetic domains

Domain behavior helps explain why some materials can become permanent magnets.

Non-Magnetic Materials

Many common materials are not strongly attracted to ordinary magnets.

Examples include:

• wood
• plastic
• glass
• paper
• rubber

Many metals are also not ferromagnetic.

For example, ordinary pieces of:

• copper
• aluminium
• gold
• silver

are not attracted strongly to a permanent magnet under everyday conditions.

This means:

metal does not automatically mean magnetic

Are All Metals Magnetic?

No.

This is a common misconception.

Iron is strongly magnetic.

Copper is not ferromagnetic.

Aluminium is not ferromagnetic.

Gold is not ferromagnetic.

Therefore, whether a material looks metallic does not determine whether it is strongly magnetic.

Its magnetic properties depend on its atomic and electronic structure.

Steel and Magnetism

Steel usually contains iron, so many types of steel are ferromagnetic.

However, different steels have different magnetic properties depending on their composition and structure.

Some steels are useful for making permanent magnets because they can retain magnetization.

Other iron-rich materials may magnetize easily but lose much of their magnetization when an external magnetic field is removed.

Magnetic Domains

A magnetic domain is a region within a ferromagnetic material in which many atomic magnetic moments are aligned in approximately the same direction.

 

 

 

7

A piece of ferromagnetic material can contain many domains.

Each domain behaves somewhat like a tiny magnetic region.

Domains in an Unmagnetized Material

In an unmagnetized piece of iron, individual domains may be internally aligned, but different domains point in different directions.

For example:

↑ ↙ → ↓ ↗ ←

The magnetic effects of the different domains largely cancel.

Therefore, the entire object may have little or no overall magnetization.

It still contains magnetic domains—the domains simply do not produce a strong net magnetic field.

Domains in a Magnetized Material

When a ferromagnetic material becomes magnetized, domains favorably aligned with the applied magnetic field grow or reorient.

The material becomes much more strongly aligned overall.

For example:

→ → → → → →

The individual magnetic contributions reinforce one another.

The object therefore develops a strong overall magnetic field.

Magnetizing a Material

A ferromagnetic material can sometimes be magnetized by exposing it to a strong magnetic field.

For example, repeatedly moving a magnet along a suitable piece of steel in the same direction can increase its magnetization.

The external magnetic field encourages domain alignment.

Afterward, some materials retain much of this alignment.

They can therefore become:

permanent magnets

Temporary Magnets

Some magnetic materials become strongly magnetized when placed in an external magnetic field but lose much of that magnetization when the field is removed.

These materials can act as:

temporary magnets

Soft iron is a useful example.

It magnetizes and demagnetizes relatively easily.

This makes it useful in devices such as:

• electromagnets
• transformers
• relays

Permanent vs Temporary Magnetism

A good permanent-magnet material retains substantial domain alignment after the external magnetizing field is removed.

A temporary magnetic material loses much of its alignment more easily.

Therefore:

permanent magnet → difficult to demagnetize

temporary magnetic material → easier to magnetize and demagnetize

Different applications require different magnetic properties.

Magnetic Domains and Atomic Magnetism

Magnetism ultimately originates from the behavior of charged particles, especially electrons.

Electrons contribute magnetic effects through their quantum properties, including their magnetic moments.

In ferromagnetic materials, interactions between neighboring atoms can cause many atomic magnetic moments to align.

This collective alignment produces magnetic domains.

Therefore, the domain model connects the large-scale behavior of magnets with microscopic atomic behavior.

Why Iron Can Be Attracted to Either Pole

Suppose an unmagnetized iron object is placed near the north pole of a magnet.

The magnet's field causes the iron to become temporarily magnetized.

The side nearest the magnet develops an effective opposite magnetic pole.

This produces attraction.

If the south pole is brought near instead, the iron's induced magnetization changes accordingly.

Therefore, an unmagnetized iron object can be attracted to:

either pole of a magnet

This is different from the interaction between two permanent magnets.

Magnetic Induction

The process in which a magnetic material becomes magnetized because it is placed in a magnetic field is called:

magnetic induction

For example:

magnet → iron nail → temporary magnetization

The nail may then attract another iron object.

 

 

 

8

Attraction Is Not Enough to Identify a Magnet

Suppose object A attracts object B.

Can we conclude that both are permanent magnets?

No.

A permanent magnet can attract an unmagnetized ferromagnetic object through magnetic induction.

A stronger test is repulsion.

If two objects repel when particular ends face each other, both must already possess magnetic polarity.

Therefore:

repulsion provides stronger evidence of permanent magnetism than attraction.

Testing Magnetic Poles

Suppose you know one end of a reference magnet is north.

Bring it near one end of an unknown magnet.

If they repel:

unknown end = north

If they attract, the unknown end may be south—but attraction alone requires care if the object has not already been established as a permanent magnet.

Once the object is known to be a magnet:

N attracts S

and:

N repels N.

Compasses

A compass contains a small permanent magnet that can rotate freely.

 

 

 

8

The compass aligns with the local magnetic field.

The north-seeking end points in the direction of the magnetic field.

Compasses can therefore be used to map the magnetic field around a permanent magnet.

Mapping a Magnetic Field

A magnetic field can be investigated using small compasses.

A simple procedure is:

1. Place a bar magnet on a surface.
2. Place a compass near the magnet.
3. Observe the direction of the compass needle.
4. Mark the field direction.
5. Move the compass to another location.
6. Repeat.
7. Connect the directions to form field lines.

The arrows outside the magnet point:

N → S

Iron Filings

Iron filings can also reveal the shape of a magnetic field.

When placed near a magnet, the filings become temporarily magnetized and tend to align with the local field.

This creates a visible pattern resembling magnetic field lines.

 

 

 

8

Iron filings show the shape of the field well, but small compasses are more useful for determining the direction of the field.

Magnetic Field Strength

The magnetic field around a permanent magnet is not equally strong everywhere.

It is generally:

• strongest near the poles
• weaker farther away

On a field-line diagram:

closer lines → stronger field

widely spaced lines → weaker field

The magnetic effect generally decreases as distance from the magnet increases.

Horseshoe Magnets

A horseshoe magnet is shaped so that its north and south poles are close together.

This produces a relatively strong magnetic field in the gap between the poles.

 

 

 

4

This design can concentrate the magnetic field in a useful region.

Demagnetization

A permanent magnet can lose some or all of its magnetization if its domain alignment is disrupted.

Possible causes include:

• strong heating
• mechanical shock
• exposure to a strong opposing magnetic field
• certain alternating magnetic fields

These processes can make the domain arrangement less aligned.

The overall magnetic field then becomes weaker.

Heating a Magnet

Increasing temperature increases thermal motion within a material.

At sufficiently high temperatures, this can disrupt the magnetic ordering responsible for ferromagnetism.

Above a material's Curie temperature, long-range ferromagnetic ordering is lost.

Cooling the material again does not automatically restore its previous permanent-magnet arrangement.

Permanent Magnets in Motors

Permanent magnets are commonly used in electric motors.

They provide a magnetic field that interacts with magnetic fields produced by electric currents.

This interaction produces forces and can generate rotational motion.

Applications include:

• small fans
• toys
• computer drives
• electric tools
• vehicle motors

Permanent Magnets in Speakers

Speakers commonly use permanent magnets.

 

 

 

7

A current passes through a coil located in the permanent magnet's magnetic field.

The interaction produces a force on the coil.

As the current changes direction and magnitude, the coil and attached speaker cone move back and forth.

This produces sound waves.

Permanent Magnets in Generators

Permanent magnets can also be used in generators.

Relative motion between:

• a magnet
• a conducting coil

can produce an induced potential difference.

This converts:

mechanical energy → electrical energy

Small generators and some renewable-energy systems use permanent magnets.

Neodymium Magnets

Neodymium magnets are powerful permanent magnets made from an alloy containing neodymium, iron, and boron.

They can produce strong magnetic fields despite their relatively small size.

Applications include:

• motors
• headphones
• speakers
• computer equipment
• sensors
• generators

Their strength also means they require careful handling.

Earth as a Magnetic Environment

Earth has a large-scale magnetic field.

A compass aligns with this field.

 

 

 

8

Earth's magnetic field is more complicated than the field of a simple bar magnet, but the bar-magnet model provides a useful first approximation.

This field allows magnetic compasses to be used for navigation.

Comparing Magnetic and Non-Magnetic Materials

Strictly speaking, many materials have weak magnetic responses, but they are not strongly ferromagnetic like iron.

Permanent Magnets vs Electromagnets

A permanent magnet produces a magnetic field without requiring continuous electrical current.

An electromagnet produces its magnetic field mainly because electric current flows through a conductor, often a coil.

Permanent magnet

• does not require continuous electrical power
• field is normally always present
• difficult to switch off
• often has relatively fixed strength

Electromagnet

• requires current
• can be switched on and off
• strength can often be adjusted
• polarity can be reversed by reversing current

Both are extremely important in modern technology.

Common Mistakes

Mistake: Saying magnets have only one pole.
Ordinary magnets have both north and south poles.

Mistake: Saying north attracts north.
Like poles repel; unlike poles attract.

Mistake: Assuming all metals are magnetic.
Many metals, including copper and aluminium, are not ferromagnetic.

Mistake: Assuming only iron is magnetic.
Nickel, cobalt and many alloys can also be ferromagnetic.

Mistake: Saying an unmagnetized piece of iron contains no magnetic domains.
It contains domains, but their overall orientations largely cancel.

Mistake: Saying magnetization creates magnetic domains.
Domains already exist in suitable ferromagnetic materials; magnetization changes their relative alignment and structure.

Mistake: Saying magnetic field lines end at the south pole.
They form continuous closed loops.

Mistake: Assuming cutting a magnet produces an isolated north and south pole.
Each piece becomes a smaller magnet with both poles.

Mistake: Assuming attraction proves that both objects are permanent magnets.
A permanent magnet can attract unmagnetized ferromagnetic material.

Key Terms

Permanent magnet — object that maintains a persistent magnetic field without continuous electrical power.

Magnetic pole — region of a magnet where its magnetic effects are especially strong.

North pole — pole from which external magnetic field lines are conventionally drawn outward.

South pole — pole into which external magnetic field lines are conventionally drawn.

Magnetic field — region where magnetic forces can act.

Magnetic field line — representation showing magnetic-field direction.

Ferromagnetic material — material capable of strong magnetic ordering, such as iron, nickel or cobalt.

Magnetic domain — region in a ferromagnetic material where many atomic magnetic moments are aligned.

Magnetization — development of an overall magnetic alignment in a material.

Magnetic induction — magnetization produced by exposure to an external magnetic field.

Temporary magnet — material that becomes magnetized relatively easily but loses much of its magnetization when the external field is removed.

Demagnetization — reduction or loss of a material's overall magnetization.

Curie temperature — temperature above which a ferromagnetic material loses its long-range ferromagnetic ordering.

Key Takeaways

• Permanent magnets produce persistent magnetic fields without requiring continuous electrical current.
• Every ordinary permanent magnet has a north and south pole.
• Like magnetic poles repel.
• Unlike magnetic poles attract.
• Magnetic forces can act without physical contact.
• Outside a magnet, magnetic field lines are conventionally drawn from north to south.
• Magnetic field lines form continuous closed loops.
• The magnetic field is generally strongest near a magnet's poles.
• Cutting a magnet produces smaller magnets, each with north and south poles.
• Iron, nickel, cobalt and many steels are ferromagnetic.
• Not all metals are strongly magnetic.
• Ferromagnetic materials contain magnetic domains.
• In an unmagnetized material, different domains are arranged so their magnetic effects largely cancel.
• Magnetization increases the overall alignment of magnetic domains.
• Some materials retain this alignment and become permanent magnets.
• Magnetic induction can temporarily magnetize a ferromagnetic object.
• Attraction alone does not prove that both objects are permanent magnets.
• Repulsion is strong evidence that two interacting objects possess magnetic poles.
• Heating, mechanical shock or opposing magnetic fields can weaken a permanent magnet.
• Permanent magnets are widely used in motors, speakers, generators, sensors and many electronic devices.

Check Your Understanding

1. Define a permanent magnet.
2. Name the two poles of a magnet.
3. What happens when two north poles are brought together?
4. What happens when a north pole and south pole are brought together?
5. State the rule describing the interaction of magnetic poles.
6. In which direction are magnetic field lines drawn outside a bar magnet?
7. Where is the magnetic field of a bar magnet generally strongest?
8. What happens if a bar magnet is cut in half?
9. Give three examples of ferromagnetic materials.
10. Explain why saying "all metals are magnetic" is incorrect.
11. Define a magnetic domain.
12. Describe the domains in an unmagnetized ferromagnetic material.
13. Describe what happens to domains when a material becomes magnetized.
14. Explain why some materials can become permanent magnets while others behave mainly as temporary magnets.
15. Explain why an unmagnetized iron nail can be attracted to either pole of a permanent magnet.
16. Why is repulsion a better test for identifying a permanent magnet than attraction?
17. Explain how iron filings can be used to investigate a magnetic field.
18. Explain how a compass can be used to determine magnetic-field direction.
19. Describe two ways in which a permanent magnet can become demagnetized.
20. Explain how the magnetic-domain model helps account for the properties of permanent magnets.

2. Magnetic field lines

Magnetic Field Lines

What Is a Magnetic Field?

A magnetic field is a region in which a magnet, magnetic material, or moving electric charge can experience a magnetic force.

Magnetic fields exist around:

• permanent magnets
• current-carrying wires
• electromagnets
• moving electric charges
• Earth and other astronomical objects

We cannot see a magnetic field directly, so diagrams use magnetic field lines to represent its direction and relative strength.

 

 

 

7

What Are Magnetic Field Lines?

A magnetic field line is an imaginary line used to represent a magnetic field.

At any point on a field line, the direction of the magnetic field is along the tangent to the line.

The arrow on the line shows the direction that the north-seeking pole of a small compass would point.

Field-line diagrams provide information about:

• field direction
• field shape
• relative field strength

Direction of Magnetic Field Lines

Outside a permanent magnet, magnetic field lines are conventionally drawn:

North → South

Therefore, field lines:

• leave the north pole
• curve through the space around the magnet
• enter the south pole

Inside the magnet, they continue:

South → North

The complete magnetic field line therefore forms a:

closed loop

Magnetic Field Lines Form Closed Loops

Magnetic field lines do not simply begin at a north pole and disappear at a south pole.

The complete path is:

N → S outside the magnet

and:

S → N inside the magnet

Therefore:

magnetic field lines form continuous closed loops.

This is an important difference from the usual field-line representation of electric charges.

Magnetic Field Around a Bar Magnet

A bar magnet produces one of the most familiar magnetic field patterns.

 

 

 

7

Outside the magnet:

• field lines emerge from N
• curve around the magnet
• enter S

The field is strongest near the poles.

The field becomes weaker as distance from the magnet increases.

How to Sketch a Bar Magnet Field

When sketching the field around a bar magnet:

1. Draw the rectangular magnet.
2. Label one end N.
3. Label the other end S.
4. Draw several curved field lines leaving N.
5. Curve the lines around toward S.
6. Add arrows showing N → S outside the magnet.
7. Draw more closely spaced lines near the poles.

A good sketch should be approximately symmetrical around the magnet.

Field-Line Density and Field Strength

The spacing of field lines represents the relative strength of the magnetic field.

closely spaced field lines → stronger field

widely spaced field lines → weaker field

For a bar magnet, the lines are usually most closely packed near the poles.

Therefore:

the magnetic field is strongest near the poles.

Field Lines Are a Model

Magnetic field lines are not physical strings or wires surrounding a magnet.

They are a representation of the magnetic field.

Drawing more lines does not actually make the field stronger.

Instead, within a single consistently drawn diagram, the relative concentration of lines represents relative field strength.

Field Direction at a Point

The magnetic field direction at any point is:

tangent to the magnetic field line

at that location.

If a field line curves, the field direction changes continuously along it.

A small compass placed at that location aligns itself approximately with the local magnetic field.

The compass's north-seeking end points along the field direction.

Using a Compass to Map a Magnetic Field

A compass can be used to investigate the field around a magnet.

 

 

 

9

A simple method is:

1. Place a bar magnet on a sheet of paper.
2. Place a small compass near the magnet.
3. Mark the direction of the compass needle.
4. Move the compass a short distance in that direction.
5. Record the new direction.
6. Repeat.
7. Connect the marks to trace a field line.
8. Repeat from several starting positions.

This produces a map of the magnetic field.

Using Iron Filings

Iron filings can also reveal the shape of a magnetic field.

When iron filings are placed near a magnet, each filing becomes temporarily magnetized.

The filings tend to align with the local magnetic field.

 

 

 

6

The pattern provides a useful visualization of:

• field shape
• regions of strong field
• regions of weaker field

However, iron filings do not clearly show field direction.

A compass is better for determining direction.

Field Around a Horseshoe Magnet

A horseshoe magnet has its north and south poles positioned relatively close together.

 

 

 

7

Between the poles, the magnetic field can be:

• relatively strong
• approximately uniform near the central region
• directed from N toward S

The close spacing of field lines between the poles represents the strong field.

Uniform Magnetic Fields

A uniform magnetic field has approximately the same:

• strength
• direction

throughout a region.

It is represented by:

straight, parallel, equally spaced field lines

For example:

→ → → → →

→ → → → →

→ → → → →

The equal spacing indicates constant field strength.

Non-Uniform Magnetic Fields

A non-uniform magnetic field changes in strength, direction, or both.

The field around a bar magnet is non-uniform.

Near a pole:

• field lines are close together
• field is strong

Farther away:

• field lines spread apart
• field becomes weaker

The field direction also changes as the lines curve.

Field Between Unlike Poles

Suppose the north pole of one magnet faces the south pole of another.

Field lines can connect from:

N → S

across the gap.

 

 

 

5

The field lines are often concentrated between the poles.

This corresponds to the attractive interaction between the magnets.

Field Between Like Poles

Suppose two north poles face each other.

The field pattern is very different.

 

 

 

5

The field lines from the two north poles curve away from the central region rather than connecting directly from one north pole to the other.

This pattern corresponds to the repulsive interaction.

A similar pattern occurs for:

S facing S

Magnetic Field Lines Never Cross

Magnetic field lines cannot cross.

Why?

At any location, the magnetic field can have only one direction.

If two field lines crossed, the intersection would imply two different magnetic-field directions at the same point.

That is impossible.

Therefore:

magnetic field lines never cross.

Magnetic Field Lines Do Not Merge or Branch

In a field-line representation, lines should also not suddenly:

• stop
• split into two
• merge randomly

They represent a continuous vector field.

For magnetic fields in particular, the field lines form continuous closed loops.

Magnetic Field Inside a Bar Magnet

Outside the magnet:

N → S

Inside the magnet:

S → N

Therefore, the complete pattern can be imagined as:

N → outside → S → inside → N

This produces a continuous loop.

Students sometimes forget the internal part of the field when sketching magnetic fields.

Magnetic Fields and Magnetic Poles

Field-line direction is defined using a hypothetical small north magnetic pole or, practically, the north-seeking end of a compass.

A north pole would experience force:

along the magnetic field

A south pole would experience force:

opposite to the magnetic field

This is similar to the way electric field direction is defined using a positive test charge.

Magnetic Field Strength

Magnetic field strength is often represented by the symbol:

B

Its SI unit is the:

tesla (T)

A larger value of B represents a stronger magnetic field.

For field-line diagrams, we usually make qualitative comparisons:

more densely packed lines → larger B

less densely packed lines → smaller B

Comparing Two Locations

Suppose point A is near the north pole of a bar magnet and point B is much farther away.

If the field lines are more closely spaced around A:

B_A > B_B

Therefore, the magnetic field at A is stronger.

The field-line diagram allows this comparison without requiring a numerical calculation.

Earth’s Magnetic Field

Earth is surrounded by a large-scale magnetic field.

 

 

 

6

A compass responds to this field and aligns approximately north-south.

Earth's actual magnetic field is more complex than that of a simple bar magnet, but the bar-magnet model provides a useful first approximation.

Magnetic Field Around a Current-Carrying Wire

Magnetic fields are not produced only by permanent magnets.

An electric current also produces a magnetic field.

Around a long straight current-carrying wire, the magnetic field lines form:

concentric circles around the wire

The field becomes weaker as distance from the wire increases.

 

 

 

9

Right-Hand Grip Rule

The direction of the magnetic field around a straight current-carrying wire can be determined using the right-hand grip rule.

Point your right thumb in the direction of:

conventional current

Your curled fingers show the direction of:

magnetic field lines

Therefore:

thumb → current

curled fingers → magnetic field

Field Around a Coil

A current-carrying coil produces a magnetic field resembling the field of a bar magnet.

One side behaves like a:

north pole

and the other behaves like a:

south pole

This is the basis of many electromagnets.

The magnetic field inside a long coil can be relatively strong and approximately uniform.

Electric Field Lines

Electric field lines represent an electric field.

For an isolated positive charge:

field lines point:

away from +

For an isolated negative charge:

field lines point:

toward −

 

Like magnetic field lines, their direction represents the direction of a force on a defined test object.

For electric fields, that test object is a:

positive test charge

Similarities Between Electric and Magnetic Field Lines

Electric and magnetic field-line diagrams share several features.

Both:

• represent invisible fields
• show field direction
• indicate relative field strength through line density
• do not cross
• show the direction of force on a defined test object
• can be used to visualize interactions at a distance

Field-line diagrams are therefore useful models in both electricity and magnetism.

Important Difference: Where the Lines Go

There is an important difference.

Electric field lines

For ordinary electrostatic diagrams, electric field lines can:

• begin on positive charges
• end on negative charges
• extend to or from infinity

Magnetic field lines

Magnetic field lines:

always form closed loops

They do not simply begin at a north pole and terminate permanently at a south pole.

Outside the magnet they travel N → S, but inside they return S → N.

Why Magnetic Field Lines Form Loops

Electric charges can exist individually.

For example, an object can have:

• net positive charge
• net negative charge

This allows electric field lines to originate or terminate on electric charge.

Ordinary magnets, however, are observed with both:

• north pole
• south pole

Cutting a magnet does not isolate the poles.

Instead, each piece develops both poles.

This is reflected by the closed-loop structure of magnetic field lines.

Electric vs Magnetic Field Lines

Comparing a Dipole with a Bar Magnet

An electric dipole consists of:

+Q and −Q

A bar magnet contains:

N and S poles

Their external field patterns can look somewhat similar.

However, there is an important distinction.

Electric field lines can begin on +Q and end on −Q.

Magnetic field lines continue through the magnet to form closed loops.

Therefore, similar-looking diagrams represent physically different fields.

Field-Line Density

Suppose two regions of the same magnetic field diagram have different line spacing.

Region A

Lines are close together.

Region B

Lines are widely separated.

Then:

field at A > field at B

provided the diagram uses a consistent field-line representation.

Field-line density provides a qualitative comparison rather than automatically giving a numerical value.

Strong and Weak Regions Around a Bar Magnet

Near the north and south poles:

field-line density is high

Therefore:

field is strong

Far from the magnet:

field-line density is lower

Therefore:

field is weaker

This is why small magnetic objects experience much stronger forces close to many permanent magnets.

Sketching Field-Line Diagrams

A good magnetic field-line diagram should follow several rules:

• include arrows showing direction
• show N → S outside a permanent magnet
• use continuous curves
• never allow lines to cross
• use closer spacing to represent stronger fields
• show appropriate symmetry where expected
• continue lines through the magnet when showing complete loops

A diagram should communicate both:

direction and relative strength

Interpreting a Field-Line Diagram

When given a magnetic field diagram, ask:

What direction does the field point?

Follow the arrows.

Where is the field strongest?

Look for the greatest field-line density.

Where is the field weakest?

Look for widely spaced lines.

Is the field uniform?

Look for straight, parallel, equally spaced lines.

Where are the poles?

Outside a permanent magnet, lines leave N and enter S.

These rules allow a large amount of information to be obtained from a simple diagram.

Example: Identifying an Unknown Pole

Suppose field-line arrows are shown leaving the left end of a magnet.

Outside a magnet:

field lines leave north

Therefore:

left end = N

The other end must be:

S

Similarly, if field lines enter an end of a magnet, that end is the south pole.

Example: Comparing Field Strength

Suppose point A has five field lines passing through a small region around it, while the same-sized region around B contains only two in a consistently drawn diagram.

We can conclude qualitatively:

B_A > B_B

The field is stronger around A.

We cannot determine an exact numerical ratio merely by counting lines unless the diagram has specifically been constructed for that purpose.

Three-Dimensional Fields

Magnetic fields exist in three dimensions.

A two-dimensional field-line diagram shows only a representation or slice of the complete field.

For example, a bar magnet's field extends:

• above the magnet
• below the magnet
• beside the magnet
• around it in three dimensions

The familiar flat diagram is therefore a simplified model of a three-dimensional field.

Why Field-Line Diagrams Are Useful

Field-line diagrams allow us to predict:

• compass orientation
• magnetic force directions
• strong and weak field regions
• interactions between magnets
• approximate uniformity of fields
• effects of changing magnet arrangements

They turn an invisible field into a model that can be analyzed visually.

Common Mistakes

Mistake: Drawing magnetic field lines from south to north outside a magnet.
Outside a magnet, they point N → S.

Mistake: Saying magnetic field lines stop at the south pole.
They continue through the magnet and form closed loops.

Mistake: Drawing magnetic field lines that cross.
A magnetic field can have only one direction at each location.

Mistake: Saying closely spaced lines represent a weak field.
Closely spaced lines represent a stronger field.

Mistake: Thinking magnetic field lines are physical objects.
They are a model used to represent a field.

Mistake: Assuming the field is equally strong everywhere around a bar magnet.
It is generally strongest near the poles.

Mistake: Drawing field lines directly from one north pole into another north pole.
Like poles produce a field pattern that bends away from the region between them.

Mistake: Assuming electric and magnetic field lines behave identically.
Magnetic field lines form closed loops, while electrostatic field lines can begin and end on charges.

Key Terms

Magnetic field — region in which magnetic forces can act.

Magnetic field line — imaginary line used to represent the direction and relative strength of a magnetic field.

Field direction — direction in which the north-seeking end of a compass would point.

Field-line density — relative concentration of field lines used to represent field strength.

Magnetic field strength — measure of the strength of a magnetic field, represented by B.

Tesla (T) — SI unit of magnetic field strength.

Uniform magnetic field — field having approximately constant strength and direction.

Non-uniform magnetic field — field whose strength or direction changes with position.

North pole — magnetic pole from which external magnetic field lines emerge.

South pole — magnetic pole into which external magnetic field lines enter.

Compass — small freely rotating permanent magnet used to determine magnetic-field direction.

Right-hand grip rule — rule used to determine magnetic-field direction around a current-carrying wire.

Electric field line — line representing the direction of an electric field.

Key Takeaways

• Magnetic field lines are used to represent magnetic fields.
• The tangent to a field line gives the magnetic-field direction at that point.
• Outside a permanent magnet, magnetic field lines point N → S.
• Inside the magnet, they return S → N.
• Magnetic field lines therefore form continuous closed loops.
• Magnetic field lines never cross.
• Closely spaced field lines represent stronger magnetic fields.
• Widely spaced field lines represent weaker magnetic fields.
• Bar magnets produce curved, non-uniform magnetic fields.
• Magnetic fields are generally strongest near the poles of permanent magnets.
• A uniform field is represented by straight, parallel, equally spaced lines.
• A compass can determine magnetic-field direction.
• Iron filings can reveal the shape of a magnetic field.
• Unlike poles produce connecting field patterns associated with attraction.
• Like poles produce field patterns that bend away from the region between them.
• Electric currents also produce magnetic fields.
• Around a straight wire, magnetic field lines form concentric circles.
• Electric and magnetic field-line diagrams both show direction and relative strength.
• Electric field lines can begin or end on electric charges.
• Magnetic field lines always form closed loops.

Check Your Understanding

1. Define a magnetic field.
2. What does a magnetic field line represent?
3. In which direction do magnetic field lines point outside a bar magnet?
4. In which direction do they travel inside the magnet?
5. Explain why magnetic field lines form closed loops.
6. Where is the magnetic field generally strongest around a bar magnet?
7. What does closely spaced field lines indicate?
8. What does widely spaced field lines indicate?
9. Why can magnetic field lines never cross?
10. Describe the magnetic field pattern around a bar magnet.
11. Describe the field pattern between opposite magnetic poles.
12. Describe the field pattern between two like magnetic poles.
13. How can a compass be used to determine magnetic-field direction?
14. How can iron filings be used to investigate a magnetic field?
15. What does a uniform magnetic field look like on a field-line diagram?
16. Describe the magnetic field around a straight current-carrying wire.
17. State the right-hand grip rule.
18. Give two similarities between electric and magnetic field-line diagrams.
19. Give one important difference between electric and magnetic field lines.
20. A student draws magnetic field lines leaving a north pole and stopping when they reach the south pole. Explain what is incorrect about the diagram.

3. Magnetic flux density

Magnetic Flux Density

What Is Magnetic Flux Density?

Magnetic flux density describes the strength and direction of a magnetic field at a particular point.

It is represented by the symbol:

B

Magnetic flux density is a vector quantity, which means it has both:

• magnitude
• direction

The direction of B is the direction shown by magnetic field lines at that point.

 

 

 

8

---

The Tesla

The SI unit of magnetic flux density is the:

tesla (T)

Named after Nikola Tesla, the tesla is used to describe the strength of magnetic fields.

For example:

B = 0.20 T

means that the magnetic flux density is:

0.20 tesla

Smaller magnetic fields are often measured using:

millitesla (mT)

or:

microtesla (μT)

Conversions:

1 T = 1000 mT

1 mT = 10⁻³ T

1 μT = 10⁻⁶ T

---

What Does a Larger B Mean?

A larger magnetic flux density means a stronger magnetic field.

For example:

B₁ = 0.80 T

B₂ = 0.20 T

Therefore:

B₁ > B₂

and the first magnetic field is stronger.

A stronger magnetic field can produce a larger force on a suitable:

• current-carrying conductor
• moving charge
• magnetic material
• magnet

under otherwise identical conditions.

---

Magnetic Flux Density and Field Lines

Magnetic field diagrams can be used to represent differences in magnetic flux density.

 

 

 

7

In a consistently drawn diagram:

closer field lines → greater magnetic flux density

widely spaced field lines → smaller magnetic flux density

Therefore, field-line density provides a visual indication of relative magnetic field strength.

---

Strong Fields Near Magnetic Poles

Around a bar magnet, magnetic field lines are usually most concentrated near the poles.

Therefore:

B is generally greatest near the poles

Farther from the magnet:

• field lines spread apart
• magnetic flux density decreases
• the field becomes weaker

This explains why a magnet usually attracts a magnetic object much more strongly when the object is close to one of its poles.

---

Magnetic Flux Density Is Not the Same as Magnetic Flux

The terms magnetic flux density and magnetic flux sound similar but describe different quantities.

Magnetic flux density

Symbol:

B

Unit:

tesla (T)

It describes the magnetic field at a location.

Magnetic flux

Symbol:

Φ

Unit:

weber (Wb)

It describes the magnetic field passing through a particular area.

For a uniform field:

Φ = BA cos θ

where θ is the angle between the magnetic field and the normal to the surface.

---

Understanding the Area Angle

The angle in:

Φ = BA cos θ

is measured between:

• the magnetic field B
• a line perpendicular to the surface, called the normal

If the field passes directly through the surface:

θ = 0°

cos 0° = 1

Therefore:

Φ = BA

If the field runs parallel to the surface:

θ = 90°

cos 90° = 0

Therefore:

Φ = 0

This distinction becomes especially important when studying electromagnetic induction.

---

Tesla and Weber

From:

Φ = BA

we can rearrange:

B = Φ/A

Therefore:

1 T = 1 Wb/m²

So a magnetic flux density of 1 tesla can be interpreted as:

1 weber of magnetic flux per square metre

when the field passes perpendicular to the area.

---

Magnetic Flux Density as a Vector

Because B is a vector, two magnetic fields with the same numerical strength may still be different if they point in different directions.

For example:

B₁ = 0.40 T east

and:

B₂ = 0.40 T west

have equal magnitudes but opposite directions.

When magnetic fields overlap, their vector directions must be considered.

---

Direction of Magnetic Flux Density

At any point, the direction of B is:

tangent to the magnetic field line

For a bar magnet, outside the magnet:

N → S

Therefore, the magnetic flux density vector points along the field lines from north toward south outside the magnet.

 

 

 

6

---

Uniform Magnetic Flux Density

A uniform magnetic field has the same magnetic flux density throughout a region.

This means B has approximately constant:

• magnitude
• direction

A uniform magnetic field is represented by:

straight, parallel, equally spaced field lines

For example:

→ → → → →

→ → → → →

→ → → → →

The constant spacing represents constant field strength.

---

Non-Uniform Magnetic Flux Density

A non-uniform magnetic field has a magnetic flux density that changes with position.

The field around a bar magnet is an example.

Near the poles:

large B

Far from the magnet:

smaller B

The direction of B also changes as the field lines curve.

---

Field Between the Poles of a Horseshoe Magnet

A horseshoe magnet places its north and south poles close together.

 

In the central region between the poles, the field lines may be:

• close together
• nearly parallel
• approximately equally spaced

This represents a relatively:

strong and approximately uniform magnetic field

---

Factors Affecting the Field of a Permanent Magnet

The magnetic flux density produced by a permanent magnet depends on several factors.

These include:

• type of magnetic material
• strength of magnetization
• size and shape of the magnet
• distance from the magnet
• location relative to the poles
• presence of other magnetic materials

A strongly magnetized material can produce a larger B than a weakly magnetized one.

---

Distance from a Magnet

Magnetic flux density generally decreases as distance from a magnet increases.

Therefore:

closer to magnet → larger B

farther from magnet → smaller B

The exact relationship depends on the shape of the magnet and where the measurement is made.

It should not automatically be assumed to follow a simple inverse-square relationship.

---

Magnetic Material

Different magnetic materials can produce very different magnetic field strengths.

Strong permanent magnets are often made from materials such as:

• neodymium-iron-boron
• samarium-cobalt
• ferrite
• alnico

Their composition and internal magnetic structure affect the magnetic flux density they can produce.

---

Magnetic Flux Density Around a Current-Carrying Wire

Electric current also produces a magnetic field.

Around a long straight wire, magnetic field lines form concentric circles.

 

 

 

8

For a long straight wire:

B = μ₀I/(2πr)

where:

• B = magnetic flux density
• μ₀ = permeability of free space
• I = current
• r = distance from the wire

This equation shows two important relationships.

---

Effect of Current

From:

B = μ₀I/(2πr)

we see:

B ∝ I

Therefore:

greater current → stronger magnetic field

If current doubles while distance remains constant:

B doubles

This is an important way of controlling the strength of electromagnets.

---

Effect of Distance from a Wire

The same equation shows:

B ∝ 1/r

Therefore:

greater distance → weaker magnetic field

For example, if the distance from a long straight wire doubles while current remains constant:

B becomes half as large

---

Example: Current and Field Strength

Suppose a wire produces:

B = 2.0 mT

at a particular distance when:

I = 3.0 A

If the current increases to:

6.0 A

while the distance remains unchanged:

current has doubled.

Since:

B ∝ I

the magnetic flux density also doubles.

Therefore:

B = 4.0 mT

---

Example: Distance from a Wire

Suppose:

B = 8.0 mT

at:

r = 2.0 cm

If the distance increases to:

r = 4.0 cm

the distance has doubled.

Since:

B ∝ 1/r

the field becomes half as strong.

Therefore:

B = 4.0 mT

---

Magnetic Field of a Solenoid

A solenoid is a long coil of wire carrying electric current.

Inside a sufficiently long solenoid, the magnetic field can be approximately uniform.

 

 

 

7

For an ideal long solenoid:

B = μ₀nI

where:

• B = magnetic flux density
• μ₀ = permeability of free space
• n = number of turns per metre
• I = current

---

Increasing the Field of a Solenoid

From:

B = μ₀nI

the magnetic field can be strengthened by:

• increasing current
• increasing the number of turns per unit length
• using a suitable magnetic core

Therefore:

larger I → larger B

and:

larger n → larger B

---

Iron Cores

Placing a ferromagnetic core such as soft iron inside a coil can greatly strengthen the magnetic field.

The coil's magnetic field encourages magnetic domains within the iron to align.

The field from the magnetized core reinforces the field produced by the coil.

This principle is used in:

• electromagnets
• transformers
• relays
• motors
• lifting magnets

---

Force on a Current-Carrying Wire

One important way to define or measure magnetic flux density involves the force on a current-carrying conductor.

For a straight conductor in a uniform magnetic field:

F = BIL sin θ

where:

• F = magnetic force (N)
• B = magnetic flux density (T)
• I = current (A)
• L = length of conductor in the field (m)
• θ = angle between current and magnetic field

If the conductor is perpendicular to the field:

θ = 90°

and:

sin 90° = 1

Therefore:

F = BIL

---

Rearranging for Magnetic Flux Density

From:

F = BIL

we can calculate:

B = F/(IL)

when the wire is perpendicular to the field.

This provides another interpretation of the tesla.

---

Meaning of One Tesla

Suppose:

I = 1 A

L = 1 m

and the conductor is perpendicular to the magnetic field.

If the magnetic force is:

F = 1 N

then:

B = F/(IL)

B = 1/(1 × 1)

B = 1 T

Therefore, a magnetic flux density of 1 T produces a force of 1 N on a 1 m conductor carrying 1 A when the conductor is perpendicular to the field.

---

Example: Calculating B from Force

A wire carries:

I = 4.0 A

A length:

L = 0.20 m

is perpendicular to a magnetic field.

The wire experiences a force:

F = 0.12 N

Use:

B = F/(IL)

B = 0.12/(4.0 × 0.20)

B = 0.12/0.80

B = 0.15 T

---

Example: Calculating Force

A wire of length:

L = 0.50 m

carries:

I = 3.0 A

perpendicular to a field:

B = 0.20 T

Use:

F = BIL

F = (0.20)(3.0)(0.50)

F = 0.30 N

---

Effect of Angle

The full equation is:

F = BIL sin θ

The force is greatest when:

θ = 90°

because:

sin 90° = 1

The force is zero when:

θ = 0°

because:

sin 0° = 0

Therefore:

current perpendicular to field → maximum force

current parallel to field → zero magnetic force

---

Magnetic Force on a Moving Charge

A moving electric charge can also experience a magnetic force.

The magnitude is:

F = Bqv sin θ

where:

• F = magnetic force
• B = magnetic flux density
• q = magnitude of charge
• v = speed of the charge
• θ = angle between velocity and magnetic field

This equation provides another way to understand what magnetic flux density represents.

---

Example: Moving Charge

A particle has:

q = 2.0 × 10⁻⁶ C

and moves at:

v = 500 m/s

perpendicular to a magnetic field:

B = 0.40 T

Use:

F = Bqv

F = (0.40)(2.0 × 10⁻⁶)(500)

F = 4.0 × 10⁻⁴ N

---

Magnetic Fields Do No Work on Moving Charges

The magnetic force on a moving charged particle is perpendicular to its velocity.

Therefore, a magnetic field can change the:

direction

of a charged particle's motion without directly changing its:

speed

or kinetic energy.

This is an important difference from electric fields, which can do work on charges and change their kinetic energy.

---

Interpreting Field Diagrams

Suppose a field diagram shows three locations:

• A: field lines very close together
• B: field lines moderately spaced
• C: field lines widely separated

Then:

B_A > B_B > B_C

Point A has the greatest magnetic flux density.

Point C has the smallest.

No numerical calculation is necessary unless numerical field values are provided.

---

Field Into and Out of the Page

Magnetic fields are three-dimensional, so diagrams need a way to represent fields perpendicular to the page.

A field pointing out of the page is represented by:

⊙

This can be imagined as seeing the point of an arrow coming toward you.

A field pointing into the page is represented by:

⊗

This can be imagined as seeing the feathers or crossed tail of an arrow moving away from you.

Therefore:

⊙ = out of page

⊗ = into page

---

Uniform Field Diagrams

A uniform field pointing into the page might appear as:

⊗ ⊗ ⊗ ⊗

⊗ ⊗ ⊗ ⊗

⊗ ⊗ ⊗ ⊗

Equal spacing indicates approximately constant B.

A uniform field pointing out of the page might appear as:

⊙ ⊙ ⊙ ⊙

⊙ ⊙ ⊙ ⊙

⊙ ⊙ ⊙ ⊙

These symbols are extremely common in magnetism problems.

---

Measuring Magnetic Flux Density

Magnetic flux density can be measured using instruments such as:

• Hall probes
• gaussmeters
• teslameters
• magnetic field sensors

 

 

 

9

A Hall probe can be moved through a magnetic field to investigate how B changes with position.

For example, students can measure B:

• near a magnet
• farther from the magnet
• between magnetic poles
• inside a solenoid

---

Magnetic Flux Density and Magnetic Flux

Consider a uniform magnetic field:

B = 0.50 T

passing perpendicular to an area:

A = 0.20 m²

Use:

Φ = BA

Φ = (0.50)(0.20)

Φ = 0.10 Wb

This means 0.10 weber of magnetic flux passes through the area.

---

Example: Finding Flux Density from Flux

Suppose:

Φ = 0.060 Wb

passes perpendicularly through:

A = 0.020 m²

Use:

B = Φ/A

B = 0.060/0.020

B = 3.0 T

---

Effect of Area

If B remains constant:

Φ = BA

Increasing the area increases the magnetic flux passing through the surface.

However, this does not mean that the magnetic flux density has increased.

The magnetic field can have the same B while a larger area intercepts more total magnetic flux.

This distinction is important.

---

Flux Density vs Flux Example

Imagine rain falling uniformly.

Magnetic flux density is somewhat analogous to:

how intensely rain is falling per unit area

Magnetic flux is somewhat analogous to:

the total amount of rain collected over an area

A larger container can collect more rain even though the rainfall intensity has not changed.

Similarly, a larger surface can have more magnetic flux through it even when B remains constant.

---

Comparing Magnetic Fields

When comparing magnetic fields, consider:

Field-line density

Closer lines usually represent larger B.

Distance from source

Fields usually weaken with increasing distance.

Current

Larger currents generally produce stronger magnetic fields.

Number of coil turns

More turns per unit length can strengthen a solenoid's field.

Magnetic core

A suitable ferromagnetic core can greatly increase B.

Magnet material

Different permanent-magnet materials can produce different field strengths.

---

Simple Problem-Solving Strategy

When solving magnetic flux density problems:

Identify the known quantities

For example:

F = 0.50 N

I = 5.0 A

L = 0.25 m

Select the correct equation

If the wire is perpendicular to the field:

B = F/(IL)

Substitute

B = 0.50/(5.0 × 0.25)

Calculate

B = 0.50/1.25

B = 0.40 T

Include the correct unit

Magnetic flux density must be expressed in:

tesla (T)

---

Multi-Step Example

A straight wire carries:

I = 2.5 A

A length:

L = 0.40 m

lies perpendicular to a magnetic field.

The magnetic force is:

F = 0.30 N

Find the magnetic flux density

B = F/(IL)

B = 0.30/(2.5 × 0.40)

B = 0.30/1.00

B = 0.30 T

Now suppose the current doubles to:

5.0 A

while B and L remain unchanged.

Find the new force

F = BIL

F = (0.30)(5.0)(0.40)

F = 0.60 N

Doubling the current doubles the force when all other factors remain constant.

---

Choosing the Correct Equation

Use:

B = F/(IL)

when finding magnetic flux density from the force on a perpendicular current-carrying conductor.

Use:

F = BIL

when the current is perpendicular to the field.

Use:

F = BIL sin θ

when the conductor is at an angle to the field.

Use:

B = μ₀I/(2πr)

for the field around an ideal long straight current-carrying wire.

Use:

B = μ₀nI

for an ideal long air-core solenoid.

Use:

Φ = BA

when a uniform field passes perpendicular to an area.

Use:

Φ = BA cos θ

when the surface is at another orientation, with θ measured from the surface normal.

---

Common Mistakes

Mistake: Saying magnetic flux density is measured in webers.
Magnetic flux density is measured in teslas. Magnetic flux is measured in webers.

Mistake: Confusing B and Φ.
B describes the magnetic field at a location; Φ describes magnetic flux through an area.

Mistake: Saying closely spaced field lines represent a weak field.
They represent a stronger field.

Mistake: Assuming field-line density provides an exact numerical B value.
Ordinary diagrams generally provide qualitative comparisons unless a scale or numerical information is supplied.

Mistake: Forgetting to convert mT to T.
1 mT = 10⁻³ T.

Mistake: Forgetting the angle in F = BIL sin θ.
The simplified equation F = BIL applies when the conductor is perpendicular to the field.

Mistake: Assuming increasing area increases B.
Increasing area can increase magnetic flux without changing magnetic flux density.

Mistake: Confusing ⊙ and ⊗.
⊙ means out of the page; ⊗ means into the page.

---

Key Terms

Magnetic flux density — vector quantity describing the strength and direction of a magnetic field at a point.

B — symbol used for magnetic flux density.

Tesla (T) — SI unit of magnetic flux density.

Magnetic field — region where magnetic forces can act.

Magnetic field line — representation showing magnetic-field direction and relative strength.

Field-line density — concentration of field lines used to represent relative magnetic field strength.

Magnetic flux — measure of magnetic field passing through an area.

Weber (Wb) — SI unit of magnetic flux.

Uniform magnetic field — field with approximately constant magnitude and direction.

Solenoid — coil of wire that produces a magnetic field when carrying current.

Hall probe — sensor used to measure magnetic flux density.

Ferromagnetic core — magnetic material placed within a coil to strengthen its magnetic field.

Permeability — property describing how a material or medium responds to a magnetic field.

---

Key Takeaways

• Magnetic flux density describes the strength and direction of a magnetic field.
• Magnetic flux density is represented by B.
• B is a vector quantity.
• The SI unit of B is the tesla (T).
• 1 mT = 10⁻³ T and 1 μT = 10⁻⁶ T.
• Larger B means a stronger magnetic field.
• Closely spaced field lines represent greater magnetic flux density.
• Magnetic fields around permanent magnets generally weaken with increasing distance.
• Around a long straight wire, increasing current increases B.
• Around a long straight wire, increasing distance decreases B.
• Increasing current strengthens the field of a solenoid.
• Increasing turns per unit length strengthens a solenoid's field.
• A ferromagnetic core can greatly increase the field of an electromagnet.
• Magnetic flux density and magnetic flux are different quantities.
• Magnetic flux density is measured in teslas.
• Magnetic flux is measured in webers.
• For a perpendicular current-carrying conductor, F = BIL.
• For a uniform field perpendicular to an area, Φ = BA.
• ⊙ represents a field out of the page.
• ⊗ represents a field into the page.

Check Your Understanding

1. Define magnetic flux density.
2. State the symbol used for magnetic flux density.
3. State the SI unit of magnetic flux density.
4. Convert 250 mT into teslas.
5. Convert 0.003 T into milliteslas.
6. What does closely spaced magnetic field lines indicate?
7. Where is B generally greatest around a bar magnet?
8. Explain how distance from a magnet affects magnetic flux density.
9. How does increasing current affect the magnetic field around a straight wire?
10. How does increasing distance from a straight current-carrying wire affect B?
11. Give three ways of increasing the magnetic field inside a solenoid.
12. Explain the difference between magnetic flux and magnetic flux density.
13. What does the symbol ⊙ represent?
14. What does the symbol ⊗ represent?
15. A 0.50 m wire carries 4.0 A perpendicular to a 0.30 T field. Calculate the magnetic force.
16. A 0.20 m wire carrying 5.0 A experiences a force of 0.40 N perpendicular to a magnetic field. Calculate B.
17. A uniform magnetic field of 0.60 T passes perpendicularly through an area of 0.25 m². Calculate the magnetic flux.
18. A magnetic flux of 0.080 Wb passes perpendicularly through an area of 0.040 m². Calculate B.
19. Explain why increasing the area through which a field passes can increase magnetic flux without increasing magnetic flux density.
20. Describe how a Hall probe could be used to investigate how magnetic flux density changes with distance from a permanent magnet.

 

 

 

4. Earth’s magnetic field

Earth’s Magnetic Field

Earth Has a Magnetic Field

Earth is surrounded by a large-scale magnetic field that extends far into space.

Near Earth's surface, the field resembles the field around a large magnetic dipole, although the real field is more complex and changes over time.

Earth's magnetic field is important because it:

• allows magnetic compasses to work
• interacts with charged particles from the Sun
• creates the magnetosphere
• contributes to the formation of auroras
• provides important information about Earth's interior

 

 

 

6

Where Does Earth's Magnetic Field Come From?

Earth is not simply a giant permanent bar magnet.

Its magnetic field is generated mainly by processes deep inside the planet.

Earth contains:

• a solid inner core
• a liquid outer core
• a rocky mantle
• a solid crust

The outer core contains mainly liquid iron and nickel.

Motion of electrically conducting material in the liquid outer core produces electric currents. These currents generate Earth's magnetic field.

This process is called the:

geodynamo

The Geodynamo

The geodynamo depends on several processes working together.

Heat escaping from Earth's interior causes liquid material in the outer core to move through convection.

Earth's rotation helps organize these flows.

Because the liquid outer core is electrically conducting, its motion can generate electric currents.

These currents create magnetic fields.

The resulting system maintains Earth's global magnetic field.

 

Earth Is Not a Permanent Magnet

It is tempting to imagine a giant bar magnet inside Earth.

The bar-magnet model is useful for understanding the general field pattern, but it is not the actual cause of Earth's magnetic field.

The temperatures inside Earth's core are far too high for the core simply to behave as an ordinary permanent iron magnet.

Instead:

moving conducting fluid → electric currents → magnetic field

Earth's Magnetic Field Lines

Earth's field can be represented using magnetic field lines.

Like all magnetic field lines, they form:

continuous closed loops

Near Earth's surface, the pattern is roughly similar to the field around a bar magnet.

However, Earth's actual field is:

• tilted relative to its rotation axis
• irregular
• changing with time
• affected by the solar wind

Geographic Poles

Earth's geographic poles are determined by Earth's axis of rotation.

They are:

Geographic North Pole

and:

Geographic South Pole

The rotation axis passes through these two points.

These are different from Earth's magnetic poles.

Magnetic Poles

Earth also has magnetic poles, determined by its magnetic field.

The magnetic poles are not located exactly at the geographic poles.

They also move over time as the processes in Earth's outer core change.

Therefore:

geographic poles ≠ magnetic poles

 

 

 

7

A Subtle Point About Magnetic North

A compass's north-seeking end points roughly toward geographic north.

Since unlike magnetic poles attract, the region near geographic north behaves, in the simple bar-magnet analogy, like a magnetic south pole.

This naming can be confusing because the location is commonly called the north magnetic pole based on its geographic location and navigation convention.

For introductory work, it is often most useful to remember:

the north-seeking end of a compass points approximately toward Earth's magnetic north region.

How a Compass Works

A compass contains a small permanent magnet that is free to rotate.

 

 

 

7

When placed in Earth's magnetic field, the compass needle experiences a turning effect.

The needle rotates until it aligns approximately with the local magnetic field.

The north-seeking end points approximately toward magnetic north.

The opposite end points approximately toward magnetic south.

Why the Compass Needle Turns

A compass needle is itself a small magnet.

Earth's magnetic field exerts forces on its magnetic poles.

If the compass is not aligned with the field, these forces produce a turning effect or torque.

The needle rotates until it aligns with the local field.

Therefore, a compass does not point north because it is somehow "pulled directly toward the North Pole."

Instead, it aligns with:

the local direction of Earth's magnetic field.

A Compass Shows Local Field Direction

The compass needle points along the horizontal component of Earth's magnetic field.

If you move to a different location on Earth, the direction of the field changes slightly.

Therefore, compass direction depends on location.

Local magnetic materials and electrical equipment can also disturb compass readings.

Examples include:

• steel structures
• vehicles
• electrical cables
• magnets
• electronic equipment

True North and Magnetic North

True north points toward the geographic North Pole.

Magnetic north is the direction indicated by Earth's magnetic field.

These directions are usually not exactly the same.

The horizontal angle between true north and magnetic north is called:

magnetic declination

Declination varies with:

• geographic location
• time

Navigators may need to account for this difference.

Magnetic Inclination

Earth's magnetic field is not usually horizontal.

The angle that the field makes with the horizontal is called:

magnetic inclination

or:

magnetic dip

Near the magnetic equatorial region, the field is more nearly horizontal.

Closer to the magnetic poles, the field becomes more steeply inclined.

A freely rotating three-dimensional magnetic needle would therefore tilt as well as turn horizontally.

Earth's Magnetic Field Strength

Earth's magnetic field is relatively weak compared with many laboratory or industrial magnets.

Near Earth's surface, its magnetic flux density is typically on the order of:

tens of microteslas (μT)

Although weak, the field extends across an enormous region of space and has major effects on charged particles around Earth.

The Magnetosphere

The region of space dominated by Earth's magnetic field is called the:

magnetosphere

 

 

 

8

The magnetosphere interacts strongly with charged particles travelling from the Sun.

It acts as an important part of Earth's space environment.

The Solar Wind

The Sun continuously releases a stream of charged particles known as the:

solar wind

The solar wind contains mainly:

• electrons
• protons
• other ions

These particles travel through interplanetary space at high speeds.

When they reach Earth, they encounter Earth's magnetic field.

How the Magnetosphere Affects the Solar Wind

Charged particles moving through a magnetic field can experience magnetic forces.

As a result, many solar-wind particles are:

• deflected
• redirected
• trapped
• guided around Earth

The magnetosphere therefore reduces the direct interaction of much of the solar wind with Earth's atmosphere.

It does not form a perfectly solid or impenetrable shield, however. Some particles can enter or become trapped within the magnetosphere.

Shape of the Magnetosphere

The solar wind changes the shape of Earth's magnetosphere.

On the side facing the Sun, the solar wind compresses the magnetic field.

This creates a relatively compressed:

dayside

On the side away from the Sun, the field is stretched into a long:

magnetotail

Therefore, the magnetosphere is not a symmetrical sphere around Earth.

 

 

 

8

Bow Shock

The solar wind moves rapidly toward Earth's magnetosphere.

The interaction creates a region called the:

bow shock

It forms on the Sun-facing side of Earth, somewhat like the shock wave produced when an object moves rapidly through a fluid.

The solar wind changes speed and direction as it encounters Earth's magnetic environment.

Magnetopause

The outer boundary separating Earth's magnetosphere from the surrounding solar wind is called the:

magnetopause

Its location is not fixed.

Changes in solar-wind pressure can compress or expand the magnetosphere.

Therefore, Earth's magnetic environment responds continuously to changing conditions from the Sun.

Charged Particles in Magnetic Fields

A moving charged particle in a magnetic field can experience a force:

F = qvB sin θ

where:

• F = magnetic force
• q = charge
• v = particle speed
• B = magnetic flux density
• θ = angle between velocity and magnetic field

The force acts perpendicular to the particle's motion and the magnetic field.

As a result, charged particles can follow curved or spiral paths around magnetic field lines.

Charged Particles Spiral Along Field Lines

Charged particles entering Earth's magnetic environment do not necessarily travel directly along magnetic field lines.

Instead, many follow spiral or helical paths around the field lines.

Their overall motion can guide them toward particular regions of Earth.

This behavior is important for understanding:

• radiation belts
• auroras
• space weather

The Van Allen Radiation Belts

Some energetic charged particles become trapped within Earth's magnetosphere.

These particles form regions known as the:

Van Allen radiation belts

 

 

 

7

The belts contain energetic charged particles influenced by Earth's magnetic field.

Understanding these regions is important for:

• satellites
• spacecraft
• astronauts
• space missions

because energetic particles can damage electronics and biological tissue.

What Are Auroras?

An aurora is a natural display of light produced in Earth's upper atmosphere.

The best-known examples are:

aurora borealis — northern lights

and:

aurora australis — southern lights

 

 

 

8

Auroras are closely connected to interactions between:

• the Sun
• Earth's magnetosphere
• charged particles
• gases in Earth's upper atmosphere

How Auroras Form

The basic process is:

solar activity → energetic charged particles → Earth's magnetic environment → upper atmosphere → light

Energetic particles can be guided toward high-latitude regions by Earth's magnetic field.

They enter the upper atmosphere and collide with atoms and molecules.

These collisions transfer energy to atmospheric particles.

Excited Atoms and Molecules

When energetic charged particles collide with atmospheric atoms and molecules, they can transfer energy to them.

The atoms or molecules enter higher-energy states.

They are then said to be:

excited

When they return to lower-energy states, they release energy as photons.

Those photons produce the visible light of an aurora.

Why Auroras Have Different Colours

Different atmospheric gases can emit different wavelengths of light.

Important gases include:

• oxygen
• nitrogen

Oxygen can produce prominent green and red emissions under suitable conditions.

Nitrogen can contribute blue, violet, and reddish colours.

The colour depends on factors such as:

• gas involved
• altitude
• energy of collisions
• atmospheric conditions

 

 

 

5

Why Auroras Usually Occur Near the Poles

Earth's magnetic field guides many energetic charged particles toward high-latitude regions.

As a result, auroras commonly occur in oval-shaped regions around Earth's magnetic poles called:

auroral ovals

This is why northern auroras are commonly seen in places such as:

• northern Canada
• Alaska
• Iceland
• Norway
• Sweden
• Finland

while southern auroras occur around Antarctica and other high southern latitudes.

Auroras and Solar Activity

The Sun's activity is not constant.

Events such as:

• solar flares
• coronal mass ejections
• changes in the solar wind

can disturb Earth's magnetosphere.

During strong disturbances, increased numbers of energetic particles may interact with Earth's upper atmosphere.

Auroras can then become:

• brighter
• more active
• visible farther from the poles

Geomagnetic Storms

A strong disturbance of Earth's magnetosphere is called a:

geomagnetic storm

Geomagnetic storms can produce spectacular auroras, but they can also affect technology.

Possible effects include:

• satellite disturbances
• communication problems
• navigation errors
• increased radiation exposure for spacecraft
• induced currents in electrical power systems

This makes Earth's magnetic field important not only scientifically but technologically.

Space Weather

Conditions produced by activity from the Sun and its interaction with Earth's magnetic environment are collectively called:

space weather

Space weather includes phenomena involving:

• solar wind
• solar flares
• coronal mass ejections
• geomagnetic storms
• auroras

Monitoring space weather helps protect technological systems.

Earth's Magnetic Field and Life

Earth's magnetosphere helps reduce the direct exposure of the atmosphere and Earth's surface to many energetic charged particles from space.

However, it should not be described as Earth's only radiation shield.

Earth's:

atmosphere

also provides extremely important protection by absorbing and interacting with incoming radiation and particles.

The magnetic field and atmosphere together contribute to Earth's protective environment.

Earth's Magnetic Poles Move

Earth's magnetic field changes because the liquid outer core is constantly moving.

As a result, the magnetic poles:

move over time

This movement is known as:

polar wander or geomagnetic secular variation, depending on the context.

Maps and navigation systems that rely on magnetic directions therefore need periodic updating.

Magnetic Reversals

Earth's magnetic field has also reversed many times during geological history.

During a geomagnetic reversal, the overall magnetic polarity changes.

The magnetic north and south orientations effectively switch.

These reversals do not happen on a simple regular schedule.

Evidence for past reversals is preserved in magnetic minerals in rocks.

Evidence from Ocean Crust

When molten rock cools, magnetic minerals can align with Earth's magnetic field and preserve information about its direction.

At mid-ocean ridges, new oceanic crust forms continuously.

Scientists discovered alternating bands of magnetic polarity on either side of these ridges.

 

 

 

7

These magnetic stripes provide important evidence for:

• past magnetic reversals
• seafloor spreading
• plate tectonics

Compasses and Navigation

For centuries, Earth's magnetic field has been used for navigation.

A compass provides a simple way of determining direction without:

• GPS
• satellites
• electronic navigation systems

However, accurate navigation may require corrections for:

• magnetic declination
• local magnetic disturbances
• changes in Earth's magnetic field

Animals and Earth's Magnetic Field

Evidence indicates that some animals can detect aspects of Earth's magnetic field.

This ability is called:

magnetoreception

It may contribute to navigation in animals such as:

• migratory birds
• sea turtles
• some fish
• certain insects

Scientists continue to investigate the exact biological mechanisms involved.

Earth's Magnetic Field vs a Bar Magnet

The bar-magnet model is useful, but Earth's magnetic field is much more complex.

Reading an Earth Magnetic-Field Diagram

When interpreting a diagram, look for:

Field direction

Follow the arrows on the magnetic field lines.

Field-line density

Closer lines indicate stronger magnetic fields.

Magnetic poles

Identify where the field becomes strongly concentrated near Earth.

Solar direction

Determine which side faces the Sun.

Magnetotail

Look for the long stretched region on the side away from the Sun.

Particle motion

Determine whether charged particles are being deflected, trapped, or guided toward the polar regions.

Magnetic Field vs Magnetosphere

These terms should not be confused.

Earth's magnetic field

The magnetic field generated mainly by processes within Earth's liquid outer core.

Magnetosphere

The large region of space around Earth in which Earth's magnetic field strongly influences charged-particle motion.

Therefore:

magnetic field = physical field

while:

magnetosphere = region dominated by that field

A Simplified Aurora Sequence

The formation of an aurora can be summarized as:

Sun

↓

solar wind and energetic particles

↓

interaction with magnetosphere

↓

particles guided toward high latitudes

↓

collisions with upper-atmosphere gases

↓

atoms and molecules become excited

↓

photons emitted

↓

aurora

This connects magnetism, atomic physics, astronomy, and atmospheric science.

Common Mistakes

Mistake: Saying Earth contains a giant permanent bar magnet.
The bar magnet is only a model. Earth's field is mainly generated by the geodynamo in the liquid outer core.

Mistake: Assuming geographic north and magnetic north are exactly the same.
They are different and their separation changes with time.

Mistake: Saying a compass points directly at the geographic North Pole.
It aligns with the local horizontal component of Earth's magnetic field.

Mistake: Saying Earth's magnetic poles never move.
They move as Earth's magnetic field changes.

Mistake: Saying the magnetosphere completely blocks the solar wind.
It deflects and redirects many charged particles, but the interaction is complex and some particles enter the magnetosphere.

Mistake: Saying auroras are produced directly by sunlight.
Auroral light is emitted by excited atmospheric atoms and molecules after interactions involving energetic charged particles.

Mistake: Saying Earth's magnetic field is Earth's only protection from space radiation.
Earth's atmosphere also provides major protection.

Mistake: Assuming Earth's magnetic field has always had its present polarity.
The field has reversed many times during Earth's geological history.

Key Terms

Earth's magnetic field — magnetic field surrounding Earth, generated mainly by motion within the liquid outer core.

Geodynamo — process by which moving electrically conducting fluid in Earth's outer core generates the planetary magnetic field.

Geographic pole — point where Earth's rotation axis intersects its surface.

Magnetic pole — region associated with Earth's magnetic field where the field is steeply directed.

Compass — small permanent magnet that aligns with the local magnetic field.

Magnetic declination — horizontal angle between magnetic north and true north.

Magnetic inclination — angle between Earth's magnetic field and the horizontal.

Magnetosphere — region of space dominated by Earth's magnetic field.

Solar wind — stream of charged particles continuously emitted by the Sun.

Magnetopause — boundary between Earth's magnetosphere and the surrounding solar wind.

Magnetotail — stretched region of Earth's magnetosphere extending away from the Sun.

Van Allen radiation belts — regions containing energetic charged particles trapped within Earth's magnetic environment.

Aurora — atmospheric light produced when energetic particles lead to excitation of atoms and molecules in the upper atmosphere.

Aurora borealis — northern aurora.

Aurora australis — southern aurora.

Geomagnetic storm — major disturbance of Earth's magnetosphere caused by solar activity.

Space weather — changing conditions in near-Earth space influenced mainly by solar activity.

Magnetoreception — ability of an organism to detect aspects of Earth's magnetic field.

Key Takeaways

• Earth is surrounded by a large-scale magnetic field.
• Earth's field is approximately dipolar near the planet but is more complex than a simple bar-magnet field.
• Earth's magnetic field is generated mainly by the geodynamo in its liquid outer core.
• Moving electrically conducting material creates currents that help generate the field.
• Geographic poles and magnetic poles are different.
• Earth's magnetic poles move over time.
• A compass is a small permanent magnet that aligns with the local magnetic field.
• Magnetic declination is the difference between magnetic north and true north.
• Earth's magnetic field extends far into space.
• The region dominated by Earth's field is called the magnetosphere.
• The solar wind contains charged particles from the Sun.
• Earth's magnetosphere deflects and redirects many solar-wind particles.
• The Sun-facing magnetosphere is compressed.
• The opposite side stretches into the magnetotail.
• Some charged particles become trapped in the Van Allen radiation belts.
• Charged particles can be guided toward Earth's polar regions.
• Collisions with atmospheric atoms and molecules can produce auroras.
• Different atmospheric gases and altitudes contribute to different auroral colours.
• Strong solar activity can produce geomagnetic storms and enhanced auroras.
• Earth's magnetic field has reversed many times during geological history.

Check Your Understanding

1. Describe Earth's magnetic field.
2. What process generates most of Earth's magnetic field?
3. Which layer of Earth is primarily responsible for the geodynamo?
4. Explain why Earth should not literally be described as a giant permanent bar magnet.
5. What is the difference between a geographic pole and a magnetic pole?
6. Explain how a compass aligns with Earth's magnetic field.
7. Why does a compass not necessarily point exactly toward geographic north?
8. Define magnetic declination.
9. What is magnetic inclination?
10. Define the magnetosphere.
11. What is the solar wind?
12. Explain how Earth's magnetosphere affects charged particles from the solar wind.
13. Why is the magnetosphere compressed on the side facing the Sun?
14. What is the magnetotail?
15. What are the Van Allen radiation belts?
16. Describe how an aurora forms.
17. Why are auroras most commonly observed near Earth's polar regions?
18. Explain why auroras can have different colours.
19. Describe one technological effect of a strong geomagnetic storm.
20. Explain how magnetic patterns in oceanic rocks provide evidence that Earth's magnetic field has reversed in the past.

5. Magnetic materials

Magnetic Materials

How Materials Respond to Magnetic Fields

Different materials respond differently when placed in a magnetic field. Some are strongly attracted to magnets, some are only weakly attracted, and others are weakly repelled.

Three important categories are:

• ferromagnetic materials
• paramagnetic materials
• diamagnetic materials

Their different behaviours arise from the magnetic properties of atoms and electrons within the material.

 

 

 

6

---

Where Magnetism Comes From

Magnetism in materials ultimately comes from electrons.

Electrons have magnetic moments associated with their quantum properties. In an atom, the magnetic effects of different electrons may:

• cancel
• partially cancel
• reinforce one another

The way these atomic magnetic moments interact determines how a material responds to an external magnetic field.

This microscopic behaviour produces the different types of magnetism we observe on a larger scale.

---

Ferromagnetic Materials

Ferromagnetic materials respond very strongly to magnetic fields and can become strongly magnetized.

Important examples include:

• iron
• nickel
• cobalt
• many steels
• some rare-earth alloys

A ferromagnetic material can be strongly attracted to a magnet.

Some ferromagnetic materials can also retain their magnetization after the external magnetic field is removed.

 

 

 

6

---

Magnetic Domains

A major feature of ferromagnetic materials is the formation of magnetic domains.

A magnetic domain is a region in which many atomic magnetic moments are aligned in approximately the same direction.

Within one domain, the magnetic effects of many atoms reinforce one another.

A piece of ferromagnetic material can contain a very large number of domains.

---

Domains in an Unmagnetized Material

An unmagnetized piece of iron still contains magnetic domains.

However, the domains may be oriented in many different directions.

For example:

↑ ↘ ← ↗ ↓ →

The magnetic effects of the domains largely cancel.

Therefore, the object has little overall magnetization.

It is incorrect to say:

"An unmagnetized material has no magnetic domains."

The domains are present; their overall magnetic effects simply cancel.

 

 

 

5

---

Domains in a Magnetized Material

When a ferromagnetic material becomes magnetized, its domain structure changes.

Domains aligned favourably with the applied magnetic field can grow, and magnetic moments can become more strongly aligned.

The material develops a net magnetization.

A simplified representation might look like:

→ → → → → →

The magnetic effects now reinforce one another instead of largely cancelling.

The object can therefore produce a strong external magnetic field.

---

How a Material Becomes Magnetized

A ferromagnetic material can be magnetized by exposing it to a sufficiently strong magnetic field.

Possible methods include:

• placing it inside a current-carrying coil
• stroking it repeatedly with a permanent magnet
• placing it close to a strong magnet

The applied field encourages the magnetic domains to become more strongly aligned.

This process is called:

magnetization

---

Magnetizing with a Solenoid

A common method of magnetization uses a solenoid.

A solenoid is a coil of wire.

When current flows through it, the coil produces a magnetic field.

If a ferromagnetic object is placed inside the solenoid, this magnetic field can cause its domains to become more aligned.

 

 

 

8

A stronger field generally produces greater magnetization until the material approaches magnetic saturation.

---

Magnetic Saturation

As the applied magnetic field becomes stronger, more of the material's magnetic structure becomes aligned.

Eventually, increasing the applied field produces relatively little additional magnetization.

The material has approached:

magnetic saturation

At saturation, the material is close to its maximum possible magnetization under those conditions.

---

Magnetic Induction

A ferromagnetic material can become temporarily magnetized when placed near a permanent magnet.

This is called:

magnetic induction

For example, an iron nail placed near a magnet can become temporarily magnetic and attract another nail.

The external magnetic field changes the domain arrangement within the iron.

When the external field is removed, the iron may lose much of its magnetization.

---

Paramagnetic Materials

Paramagnetic materials are weakly attracted to an external magnetic field.

Examples include:

• aluminium
• magnesium
• platinum
• oxygen

Their magnetic response is much weaker than that of ferromagnetic materials.

 

 

 

6

In a paramagnetic material, atomic magnetic moments tend to align slightly with an applied magnetic field.

However, thermal motion prevents strong long-range alignment.

When the external field is removed, the material generally does not remain strongly magnetized.

---

Paramagnetic Behaviour

Without an external field, the atomic magnetic moments of a paramagnetic material are largely randomly oriented.

When a magnetic field is applied:

some moments tend to align with the field

This produces a weak net magnetization in the same direction as the applied field.

Therefore:

paramagnetic materials are weakly attracted toward stronger magnetic fields.

---

Diamagnetic Materials

Diamagnetic materials are weakly repelled by magnetic fields.

Examples include:

• bismuth
• copper
• silver
• gold
• water
• graphite

When an external magnetic field is applied, it induces a very small magnetic response in the material that opposes the applied field.

Therefore:

diamagnetic materials are weakly repelled from stronger magnetic fields.

 

 

 

8

---

Diamagnetism

Diamagnetism occurs because an applied magnetic field changes the motion of electrons within atoms.

The resulting induced magnetic effect opposes the applied field.

This is related to a general physical tendency for induced magnetic effects to oppose the change that produces them.

The effect is usually extremely weak.

However, in strong magnetic fields it can become observable.

---

All Materials Have Some Diamagnetic Response

Diamagnetism is a fundamental response found in matter.

However, in materials that are strongly ferromagnetic or paramagnetic, those stronger magnetic effects usually dominate.

Therefore, we normally classify a material according to the dominant magnetic behaviour that is experimentally observed.

---

Comparing the Three Types

Property	Ferromagnetic	Paramagnetic	Diamagnetic
Response to field	Strong attraction	Weak attraction	Weak repulsion
Net response	With applied field	With applied field	Opposes applied field
Can retain strong magnetization?	Often possible	Generally no	No
Domain behaviour important?	Yes	Not in the same ferromagnetic-domain sense	Not in the same ferromagnetic-domain sense
Example	Iron	Aluminium	Copper
Relative effect	Very strong	Weak	Very weak

---

A Common Misconception About Aluminium

Aluminium is often casually described as "non-magnetic."

For everyday situations, this is usually reasonable because ordinary magnets do not strongly attract aluminium.

More precisely, however:

aluminium is paramagnetic

Its attraction to a magnetic field is simply much weaker than the attraction experienced by ferromagnetic iron.

Similarly, copper is diamagnetic rather than completely unaffected by magnetic fields.

---

Magnetic Susceptibility

A material's response to an applied magnetic field can be described using magnetic susceptibility.

It is commonly represented by:

χ

Very broadly:

ferromagnetic → very large positive response

paramagnetic → small positive χ

diamagnetic → small negative χ

A positive susceptibility means the induced magnetization tends to align with the applied field.

A negative susceptibility means the induced response tends to oppose it.

---

Soft Magnetic Materials

A soft magnetic material is easy to:

• magnetize
• demagnetize

Soft magnetic materials respond readily when an external magnetic field changes.

They are useful when magnetism must be repeatedly switched or reversed.

Examples include:

• soft iron
• silicon steel
• some ferrites

 

 

 

9

---

Applications of Soft Magnetic Materials

Soft magnetic materials are useful in:

• electromagnets
• transformers
• electric motors
• generators
• relays
• inductors

For example, an electromagnet should become strongly magnetized when current flows but lose much of that magnetization when the current is switched off.

A soft magnetic material is ideal for this purpose.

---

Hard Magnetic Materials

A hard magnetic material is more difficult to magnetize, but once strongly magnetized it resists demagnetization.

Hard magnetic materials retain a large amount of their magnetization.

They are therefore useful for making:

permanent magnets

Examples include suitable:

• hard steels
• neodymium-iron-boron alloys
• samarium-cobalt alloys
• some ferrites
• alnico alloys

---

Applications of Hard Magnetic Materials

Hard magnetic materials are used when a persistent magnetic field is required.

Applications include:

• permanent magnets
• speakers
• headphones
• electric motors
• generators
• magnetic sensors
• magnetic fasteners
• data and position-sensing systems

 

 

 

9

---

Soft vs Hard Magnetic Materials

Soft Magnetic Materials	Hard Magnetic Materials
Easy to magnetize	Generally harder to magnetize strongly
Easy to demagnetize	Difficult to demagnetize
Low magnetic coercivity	High magnetic coercivity
Useful with changing fields	Useful for permanent fields
Electromagnets	Permanent magnets
Transformer cores	Speakers and permanent-magnet motors

The words soft and hard refer to magnetic behaviour, not necessarily mechanical softness or hardness.

---

Retentivity

Retentivity, or remanence, describes a material's ability to retain magnetization after the external magnetizing field is removed.

A permanent-magnet material should have substantial remanent magnetization.

Soft magnetic materials are generally designed to retain relatively little magnetization after the applied field is removed.

---

Coercivity

Coercivity describes how strongly a material resists being demagnetized.

A hard magnetic material has:

high coercivity

A soft magnetic material has:

low coercivity

Therefore:

high coercivity → good for permanent magnets

low coercivity → good for transformer and electromagnet cores

---

Hysteresis

When a ferromagnetic material is repeatedly magnetized in opposite directions, its magnetization does not respond instantaneously to the changing applied field.

This behaviour is called:

magnetic hysteresis

It can be represented using a hysteresis loop.

 

 

 

5

The shape of the loop tells us about important properties such as:

• remanence
• coercivity
• energy losses

---

Soft Materials and Hysteresis

Soft magnetic materials generally have a relatively:

narrow hysteresis loop

This means relatively little energy is lost when the material is repeatedly magnetized and demagnetized.

That is important in transformers, where the magnetic field reverses many times every second.

Reducing hysteresis losses improves efficiency.

---

Hard Materials and Hysteresis

Hard magnetic materials generally have a wider hysteresis loop and high coercivity.

This means they resist changes to their magnetization.

That is useful for permanent magnets because the material should maintain its magnetic state despite:

• external magnetic fields
• vibration
• ordinary environmental changes

---

Transformer Cores

Transformers require a magnetic field that changes continuously with alternating current.

The core should:

• magnetize easily
• demagnetize easily
• reverse its magnetization repeatedly
• lose as little energy as practical

Therefore, transformer cores use suitable:

soft magnetic materials

 

 

 

7

---

Electromagnets

An electromagnet usually contains a coil surrounding a soft ferromagnetic core.

When current flows:

current → magnetic field → core magnetizes → stronger magnetic field

When the current stops, the core should lose most of its magnetization.

Applications include:

• scrapyard lifting magnets
• relays
• magnetic locks
• bells
• solenoid actuators

---

Permanent-Magnet Motors

Permanent-magnet motors use hard magnetic materials to provide a persistent magnetic field.

The permanent magnet interacts with magnetic fields produced by electric currents.

This interaction produces forces that can generate rotation.

Strong rare-earth magnets allow powerful motors to be made relatively small.

Applications include:

• electric vehicles
• drones
• computer equipment
• power tools
• robotics

---

Speakers and Headphones

Speakers often contain a permanent magnet made from a hard magnetic material.

A current-carrying coil sits within the magnetic field.

The interaction between the current and magnetic field produces a force.

The coil moves a diaphragm or cone, creating sound waves.

Permanent magnets are useful because they provide the required magnetic field without continuous electrical power.

---

Magnetic Data Storage

Magnetic materials can also represent information.

In magnetic storage systems, small regions of material can have different magnetization states.

These states can represent digital information.

Magnetic storage has been used in technologies such as:

• hard disk drives
• magnetic tape
• magnetic stripes

The material must maintain its magnetic state reliably until deliberately changed.

---

Magnetic Shielding

Some magnetic materials are useful for controlling the path of magnetic fields.

Materials with suitable magnetic properties can provide a preferred path for magnetic flux.

This can reduce magnetic-field strength in a protected region.

Magnetic shielding is useful around:

• sensitive instruments
• sensors
• electronic equipment
• scientific experiments

---

Magnetic Sensors

Magnetic materials and magnetic-field effects are used in many sensors.

Applications include:

• vehicle wheel-speed sensing
• position detection
• door sensors
• current measurement
• compasses
• industrial automation

Magnetic sensing is useful because it can often work without physical contact between moving parts.

---

Heating and Ferromagnetism

Heating can affect magnetic ordering.

As temperature increases, thermal motion makes magnetic alignment more difficult.

Above a characteristic temperature called the:

Curie temperature

a ferromagnetic material loses its long-range ferromagnetic ordering.

It then behaves differently magnetically.

The Curie temperature depends on the material.

---

Demagnetizing a Material

A magnetized material can be demagnetized by disrupting its magnetic alignment.

Methods can include:

• strong heating
• mechanical shock
• applying an opposing magnetic field
• applying an alternating magnetic field that gradually decreases

The goal is to reduce the material's overall magnetic alignment.

---

Magnetizing by Stroking

A simple classroom method involves repeatedly moving one pole of a permanent magnet along a ferromagnetic object in the same direction.

The repeated applied magnetic field encourages greater domain alignment.

The object can then develop an overall north and south pole.

This works much better with suitable ferromagnetic materials than with paramagnetic or diamagnetic materials.

---

Magnetizing by Electric Current

A stronger and more controllable method is to place a ferromagnetic object inside a solenoid.

When current flows:

electric current → magnetic field → domain alignment

Increasing the current can increase the applied magnetic field.

The resulting magnetization depends on:

• material
• applied field strength
• previous magnetic history
• temperature

---

Choosing a Magnetic Material

Engineers select magnetic materials according to the job they need to perform.

For an electromagnet:

soft magnetic material

is generally preferred.

For a permanent magnet:

hard magnetic material

is preferred.

For a transformer:

soft material with low hysteresis loss

is desirable.

For a compact powerful permanent-magnet motor:

strong hard magnetic material

may be desirable.

Material selection is therefore an important part of engineering design.

---

Common Mistakes

Mistake: Calling every material attracted to a magnet ferromagnetic.
Paramagnetic materials are also attracted, but much more weakly.

Mistake: Saying diamagnetic means completely non-magnetic.
Diamagnetic materials respond weakly by opposing an applied magnetic field.

Mistake: Saying an unmagnetized ferromagnetic material has no magnetic domains.
It has domains, but their overall magnetic effects largely cancel.

Mistake: Saying magnetization creates domains.
Magnetization mainly changes domain structure and alignment.

Mistake: Assuming aluminium is ferromagnetic because it is a metal.
Aluminium is paramagnetic.

Mistake: Assuming copper has no magnetic response.
Copper is diamagnetic.

Mistake: Thinking "soft magnetic" means physically soft.
It refers to how easily the material can be magnetized and demagnetized.

Mistake: Thinking "hard magnetic" simply means mechanically hard.
It refers primarily to resistance to changes in magnetization.

Mistake: Using hard magnetic material for every electromagnet.
Electromagnets generally require materials that can magnetize and demagnetize readily.

---

Key Terms

Magnetic material — material that responds to an applied magnetic field.

Ferromagnetic — strongly magnetic behaviour involving cooperative alignment of magnetic moments.

Paramagnetic — weak attraction to a magnetic field caused by partial alignment of atomic magnetic moments.

Diamagnetic — weak magnetic response that opposes an applied magnetic field.

Magnetic domain — region of a ferromagnetic material containing many similarly aligned magnetic moments.

Magnetization — overall magnetic moment per unit volume, or more generally the process/state of producing magnetic alignment in a material.

Magnetic induction — magnetization caused by exposure to an external magnetic field.

Magnetic saturation — condition in which increasing the applied field produces relatively little further magnetization.

Soft magnetic material — material that can be magnetized and demagnetized relatively easily.

Hard magnetic material — material that strongly resists demagnetization and is suitable for permanent magnets.

Remanence — magnetization remaining after an external magnetizing field is removed.

Coercivity — measure of a material's resistance to demagnetization.

Hysteresis — lagging behaviour of magnetization as an applied magnetic field changes.

Hysteresis loop — graph showing magnetic response during a complete cycle of magnetization.

Curie temperature — temperature above which long-range ferromagnetic ordering disappears.

---

Key Takeaways

• Materials respond differently to magnetic fields.
• Ferromagnetic materials are strongly attracted to magnetic fields.
• Iron, nickel and cobalt are important ferromagnetic materials.
• Paramagnetic materials are weakly attracted to magnetic fields.
• Aluminium is an example of a paramagnetic material.
• Diamagnetic materials are weakly repelled by magnetic fields.
• Copper and bismuth are examples of diamagnetic materials.
• Ferromagnetic materials contain magnetic domains.
• Domains contain many similarly aligned atomic magnetic moments.
• In an unmagnetized ferromagnetic material, domain contributions largely cancel.
• Magnetization changes the domain structure so the material develops a net magnetic effect.
• Strong fields can eventually drive a material toward magnetic saturation.
• Soft magnetic materials magnetize and demagnetize easily.
• Soft magnetic materials are useful in transformers and electromagnets.
• Hard magnetic materials resist demagnetization.
• Hard magnetic materials are useful for permanent magnets.
• High coercivity is important for permanent-magnet materials.
• Low coercivity is useful when magnetization must change repeatedly.
• Hysteresis can cause energy losses in magnetic materials.
• Magnetic materials are essential in motors, generators, transformers, speakers, sensors, data storage and many other technologies.

Check Your Understanding

1. Name the three major categories of magnetic materials discussed in these notes.
2. Define a ferromagnetic material.
3. Give three examples of ferromagnetic materials.
4. Define a paramagnetic material.
5. Give one example of a paramagnetic material.
6. Define a diamagnetic material.
7. Give two examples of diamagnetic materials.
8. Explain the difference between the response of paramagnetic and diamagnetic materials to an external magnetic field.
9. What is a magnetic domain?
10. Describe the domain arrangement in an unmagnetized ferromagnetic material.
11. Explain what happens to the domain structure when a ferromagnetic material becomes magnetized.
12. Describe one method of magnetizing a ferromagnetic material.
13. What is magnetic saturation?
14. Explain the difference between soft and hard magnetic materials.
15. Why is soft iron useful in an electromagnet?
16. Why are hard magnetic materials suitable for permanent magnets?
17. Define coercivity.
18. Explain why a transformer requires a soft magnetic material with relatively low hysteresis loss.
19. Give three technological applications of magnetic materials and explain why the chosen magnetic properties are useful in each.
20. Explain why the statement "copper and aluminium are completely non-magnetic" is scientifically inaccurate.