Electromagnetism
1. Magnetic Fields from Currents
Learning outcomes
- I can describe how electric currents produce magnetic fields.
- I can determine magnetic field direction using the right-hand grip rule.
- I can sketch magnetic field patterns around current-carrying conductors.
- I can explain Oersted's discovery.
- I can compare magnetic fields from wires and permanent magnets.
Magnetic Fields from Currents
Electric Current Produces a Magnetic Field
Whenever electric charge moves, it produces a magnetic field.
Therefore, a wire carrying an electric current is surrounded by a magnetic field.
This is one of the fundamental connections between electricity and magnetism:
electric current → magnetic field
The field exists around the conductor whenever current flows and disappears when the current stops.
Oersted's Discovery
In 1820, Danish physicist Hans Christian Oersted discovered an important connection between electricity and magnetism.
During a demonstration involving an electric circuit, he noticed that a nearby compass needle moved when current flowed through a wire.
When the current was switched off, the compass returned toward its normal north–south direction.
When the current direction was reversed, the compass deflected in the opposite direction.
This provided strong evidence that:
an electric current produces a magnetic field.
Why Oersted's Discovery Was Important
Before Oersted's experiment, electricity and magnetism were often studied as largely separate phenomena.
His observation showed that they are connected.
The discovery helped lead to the development of:
- electromagnetism
- electromagnets
- electric motors
- generators
- transformers
- modern electrical technology
Oersted's experiment was therefore an important step toward our modern understanding of electromagnetic interactions.
Recreating Oersted's Experiment
A simple version of the experiment requires:
- straight wire
- battery or power supply
- switch
- compass
Place the compass close to the wire.
With the current switched off, the compass aligns mainly with Earth's magnetic field.
Switch the current on.
The compass needle changes direction because it now responds to the combined magnetic field from:
- Earth
- current-carrying wire
Reverse the current.
The compass deflects in the opposite direction.
Magnetic Field Around a Straight Wire
The magnetic field around a long, straight current-carrying wire forms:
concentric circles
The circles are centred on the wire.
This is very different from the curved north-to-south field pattern around a bar magnet.
If viewed from one end of the wire, the magnetic field appears as circular loops surrounding the current.
Three-Dimensional Field Pattern
Imagine a straight wire passing vertically through a horizontal sheet of paper.
The magnetic field lines form circles around the wire in the plane of the paper.
The farther the field lines are from the wire, the weaker the field becomes.
The field therefore surrounds the entire wire in three dimensions.
Right-Hand Grip Rule
The right-hand grip rule determines the direction of the magnetic field around a current-carrying conductor.
Grip the wire with your right hand.
Point your thumb in the direction of:
conventional current
Your curled fingers show the direction of:
magnetic field
Remember:
thumb → current
curled fingers → magnetic field
Current Out of the Page
The symbol:
⊙
means current is travelling:
out of the page
Imagine the point of an arrow coming toward you.
Using the right-hand grip rule:
thumb → toward you
fingers curl:
counterclockwise
Therefore:
current out of page ⊙ → magnetic field counterclockwise
Current Into the Page
The symbol:
⊗
means current is travelling:
into the page
Imagine seeing the crossed tail of an arrow moving away from you.
Using the right-hand grip rule:
thumb → into page
fingers curl:
clockwise
Therefore:
current into page ⊗ → magnetic field clockwise
A Useful Direction Summary
⊙ current out of page → field counterclockwise
⊗ current into page → field clockwise
These relationships are extremely useful when sketching magnetic fields around wires.
Sketching the Field Around a Straight Wire
When sketching the field:
- Draw the wire.
- Show the direction of conventional current.
- Draw circular field lines centred on the wire.
- Use the right-hand grip rule.
- Add arrows showing field direction.
- Draw field lines closer together near the wire to indicate a stronger field.
A correct sketch should show:
concentric circular magnetic field lines
rather than lines radiating outward from the wire.
Field Strength Around a Straight Wire
For a long straight wire:
B = μ₀I/(2πr)
where:
- B = magnetic flux density (T)
- μ₀ = permeability of free space
- I = current (A)
- r = perpendicular distance from the wire (m)
The constant:
μ₀ = 4π × 10⁻⁷ T·m/A
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:
magnetic field strength doubles
provided the distance from the wire remains unchanged.
Effect of Distance
The equation also shows:
B ∝ 1/r
Therefore:
greater distance from wire → weaker magnetic field
If the distance doubles:
magnetic field strength halves
This is why the field lines are commonly drawn closer together near the wire.
Example: Changing Current
Suppose a wire produces a magnetic flux density:
B = 2.0 × 10⁻⁵ T
at a particular distance.
The current is then tripled.
Since:
B ∝ I
the new field is:
B = 3(2.0 × 10⁻⁵)
B = 6.0 × 10⁻⁵ T
Example: Changing Distance
A wire produces:
B = 4.0 × 10⁻⁵ T
at:
r = 0.10 m
What happens at:
r = 0.20 m?
The distance has doubled.
Since:
B ∝ 1/r
the field strength halves:
B = 2.0 × 10⁻⁵ T
Example: Calculating Magnetic Flux Density
A straight wire carries:
I = 5.0 A
Find the magnetic flux density:
r = 0.020 m
from the wire.
Use:
B = μ₀I/(2πr)
B = [(4π × 10⁻⁷)(5.0)]/[2π(0.020)]
Cancel π:
B = (20 × 10⁻⁷)/(0.040)
B = 5.0 × 10⁻⁵ T
or:
B = 50 μT
Reversing the Current
If the current direction is reversed, the magnetic field direction also reverses.
For example:
current out of page → counterclockwise field
Reverse current:
current into page → clockwise field
The shape of the field remains circular, but the arrows point in the opposite direction.
Magnetic Field from a Loop of Wire
If a wire is bent into a circular loop, every section of the wire produces a magnetic field.
These fields combine.
At the centre of the loop, the fields reinforce one another.
The resulting field is stronger than the field produced by a single straight section of wire at a comparable distance.
Right-Hand Rule for a Current Loop
Curl the fingers of your right hand in the direction of conventional current around the loop.
Your thumb points toward the loop's:
magnetic north direction
and along the magnetic field through the centre of the loop.
This shows how a current loop begins to behave like a small magnet.
Magnetic Field of a Coil
Several loops placed together form a:
coil
The magnetic fields from the individual loops combine.
If many loops are arranged closely together, they can produce a much stronger and more organized magnetic field.
This leads to the:
solenoid
Solenoids
A solenoid is a long coil containing many turns of wire.
When current flows through it, the magnetic fields from all the loops combine.
The resulting magnetic-field pattern resembles the field of a:
bar magnet
A solenoid has:
- a north pole
- a south pole
- a relatively strong field inside the coil
- a weaker curved field outside
Field Inside a Solenoid
For an ideal long solenoid:
B = μ₀nI
where:
- B = magnetic flux density (T)
- μ₀ = permeability of free space
- n = number of turns per metre
- I = current (A)
This means:
B ∝ n
and:
B ∝ I
Therefore, the magnetic field can be strengthened by:
- increasing current
- increasing the number of turns per unit length
Determining Solenoid Poles
The right-hand grip rule can also be used for a solenoid.
Curl your right-hand fingers in the direction of conventional current around the coil.
Your thumb points toward the:
north pole of the solenoid
This is closely related to the right-hand rule for a current loop.
Clockwise and Counterclockwise Current in a Coil
When looking directly at one end of a solenoid:
counterclockwise current → north pole
clockwise current → south pole
This is a useful shortcut when identifying solenoid poles.
Adding an Iron Core
Placing a ferromagnetic core such as soft iron inside a current-carrying coil can greatly increase its magnetic field.
The external field helps align magnetic domains inside the iron.
The magnetized iron then contributes its own magnetic field.
The combination produces a much stronger field.
This creates an:
electromagnet
Electromagnets
An electromagnet is a magnet whose field is produced primarily by electric current.
Unlike a permanent magnet, an electromagnet can be controlled.
It can be:
- switched on
- switched off
- strengthened
- weakened
- reversed
This makes electromagnets extremely useful.
Increasing Electromagnet Strength
The magnetic field can generally be strengthened by:
Increasing current
larger I → stronger field
Increasing number of coil turns
more turns → stronger combined field
Using a suitable ferromagnetic core
A soft iron core greatly strengthens the magnetic field.
Reducing excessive gaps
Magnetic-field geometry also affects practical electromagnet strength.
Reversing an Electromagnet
If the current through a solenoid is reversed:
- magnetic-field direction reverses
- north pole becomes south
- south pole becomes north
Therefore, electromagnet polarity can be controlled electrically.
This is an important advantage over many permanent magnets.
Field Around a Straight Wire vs a Solenoid
A straight wire produces:
circular field lines around the wire
A solenoid produces:
a field pattern similar to a bar magnet
Inside a long solenoid, the field is approximately:
uniform
This means the field has nearly constant:
- strength
- direction
over much of the interior.
Current-Carrying Wire vs Permanent Magnet
Both current-carrying wires and permanent magnets produce magnetic fields.
However, their field patterns are different.
| Current-Carrying Straight Wire | Permanent Bar Magnet |
|---|---|
| Field forms circles around wire | Field loops from N to S outside magnet |
| Requires electric current | Can maintain field without external current |
| Direction depends on current direction | Direction depends on pole orientation |
| Strength depends on current and distance | Strength depends on magnet/material and distance |
| Field disappears when current stops | Field normally remains |
Solenoid vs Permanent Magnet
A solenoid is more directly comparable to a bar magnet.
Both have:
- north and south poles
- similar external field patterns
- field lines forming closed loops
However, a solenoid's field can be controlled by changing the current.
Similarity Between Solenoids and Bar Magnets
Outside a bar magnet, magnetic field lines travel approximately:
north → south
A current-carrying solenoid produces a similar external pattern.
Inside both systems, the field continues back toward the north side so that magnetic field lines form:
closed loops
This similarity demonstrates how electric currents can reproduce magnetic-field patterns normally associated with permanent magnets.
Why Permanent Magnets Also Involve Moving Charge
At the microscopic level, magnetism in materials is associated with magnetic moments related to electrons.
In ferromagnetic materials, many atomic magnetic moments can align into magnetic domains.
Therefore, permanent magnetism and current-produced magnetism are not completely unrelated phenomena.
Both ultimately arise from electromagnetic properties associated with charged particles.
Two Parallel Current-Carrying Wires
Since each current-carrying wire produces a magnetic field, two nearby wires can interact magnetically.
Each wire lies in the magnetic field produced by the other.
This produces forces between the wires.
For parallel wires:
currents in same direction → attraction
currents in opposite directions → repulsion
Why Parallel Wires Interact
Consider wire A.
It produces a magnetic field around itself.
Wire B lies inside that magnetic field.
Because wire B carries current, it experiences a magnetic force.
At the same time, wire B creates a field that acts on wire A.
The wires therefore exert forces on each other.
This connects two important ideas:
current produces magnetic field
and:
magnetic field exerts force on current
Superposition of Magnetic Fields
If several currents or magnets produce fields in the same region, the resulting magnetic field is the vector sum of the individual fields.
This is called:
superposition
At some locations, fields may reinforce each other.
At others, they may oppose each other.
This principle helps explain the field patterns produced by:
- loops
- coils
- solenoids
- multiple wires
- electric motors
- electromagnets
Field Between Two Wires
Suppose two parallel wires carry current in the same direction.
Between the wires, their magnetic fields point in opposite directions.
Outside the pair, parts of the fields reinforce.
If the currents flow in opposite directions, the pattern changes.
Understanding these combined fields helps explain the attraction and repulsion between current-carrying wires.
Magnetic Field Mapping
The field around a wire can be investigated using small compasses.
Place several compasses around a vertical current-carrying wire.
Each compass aligns approximately with the local magnetic field.
Together, the compass directions reveal a circular pattern.
Reversing the current reverses all the compass directions.
This provides direct experimental evidence for the right-hand grip rule.
Iron Filings and Current-Carrying Conductors
Iron filings can also reveal magnetic-field patterns.
When placed near a current-carrying conductor, the filings tend to align with the local magnetic field.
Around a straight wire, they can reveal approximately:
circular patterns
Around a solenoid, they reveal a pattern resembling that of a bar magnet.
Compasses are better for showing the direction of the field because iron filings mainly show its shape.
Magnetic Field Direction and Conventional Current
The right-hand grip rule uses:
conventional current
Conventional current is defined as the direction positive charge would move.
In metallic wires, electrons actually drift in the opposite direction.
Therefore:
conventional current direction ≠ electron drift direction
For standard magnetic-field calculations and right-hand rules, use conventional current unless told otherwise.
Example: Finding Field Direction
A straight wire carries current upward.
Point your right thumb:
upward
Your fingers curl around the wire.
At a point directly in front of the wire, the magnetic field has one direction.
At a point directly behind the wire, it has the opposite direction.
This occurs because the field forms circles around the conductor.
Example: Current Into the Page
A wire carries current:
⊗
This means current travels into the page.
Use the right-hand grip rule.
The magnetic field circles:
clockwise
Therefore, when sketching:
⊗ at centre
with clockwise arrows around it.
Example: Current Out of the Page
A wire carries current:
⊙
This means current travels out of the page.
Use the right-hand grip rule.
The magnetic field circles:
counterclockwise
Therefore:
⊙ at centre
with counterclockwise arrows around it.
Practical Applications
Magnetic fields produced by electric currents are fundamental to many technologies.
Examples include:
- electromagnets
- electric motors
- generators
- transformers
- relays
- loudspeakers
- magnetic locks
- MRI systems
- particle accelerators
- electromagnetic lifting systems
Many modern technologies rely on our ability to create and control magnetic fields using electric currents.
Electromagnetic Cranes
Industrial cranes can use large electromagnets to lift ferromagnetic materials such as iron and steel.
Current switched on:
strong magnetic field → metal attracted
Current switched off:
field greatly decreases → load released
This ability to control magnetism electrically makes electromagnets particularly useful.
Relays
A relay can use an electromagnet to operate an electrical switch.
Current through a coil produces a magnetic field.
The field attracts a ferromagnetic armature.
The moving armature opens or closes electrical contacts.
Therefore, a relatively small electrical signal can control another circuit.
Loudspeakers and Motors
The relationship between currents and magnetic fields is central to both motors and loudspeakers.
A current produces a magnetic field.
That field interacts with another magnetic field.
The resulting magnetic force produces:
- rotation in motors
- vibration in loudspeakers
This shows how the topics of magnetic fields from currents and magnetic forces fit together.
Common Mistakes
Mistake: Drawing field lines radiating outward from a straight wire.
The magnetic field forms circles around the wire.
Mistake: Using the left hand to find the field around a wire.
Use the right-hand grip rule.
Mistake: Pointing the thumb in the magnetic-field direction.
For a straight wire, the thumb points in the current direction and the curled fingers show the magnetic field.
Mistake: Using electron-flow direction instead of conventional current.
Use conventional current unless specifically told otherwise.
Mistake: Saying current out of the page produces a clockwise field.
Out of the page produces a counterclockwise field.
Mistake: Saying the magnetic field becomes stronger farther from a straight wire.
The field becomes weaker with increasing distance.
Mistake: Saying a solenoid has no poles because it is made from wire.
A current-carrying solenoid behaves similarly to a bar magnet and has north and south poles.
Mistake: Saying Oersted discovered that magnets produce electricity.
His famous observation showed that electric current produces a magnetic field.
Mistake: Assuming a compass points directly toward a wire.
It aligns with the local magnetic field, which circles the wire.
Key Terms
Current — rate of flow of electric charge.
Magnetic field — region in which magnetic forces can act.
Magnetic flux density (B) — measure of magnetic-field strength and direction, measured in teslas.
Oersted's experiment — experiment demonstrating that electric current produces a magnetic field.
Right-hand grip rule — rule used to determine magnetic-field direction around a current-carrying conductor.
Conventional current — defined direction of positive-charge flow.
Concentric circles — circles sharing the same centre; the pattern formed by magnetic field lines around a straight wire.
Current loop — circular conductor carrying current and producing a magnetic field.
Coil — conductor wound into multiple loops.
Solenoid — long coil of wire that produces a bar-magnet-like magnetic field when carrying current.
Electromagnet — magnet produced using electric current, often strengthened with a ferromagnetic core.
Magnetic domain — region in a ferromagnetic material in which many magnetic moments are aligned.
Superposition — principle that the total magnetic field is the vector sum of individual magnetic fields.
Permeability — property related to how a material or medium responds to a magnetic field.
Key Takeaways
- Electric currents produce magnetic fields.
- Oersted demonstrated the connection between electricity and magnetism using a current-carrying wire and compass.
- A straight current-carrying wire produces circular magnetic field lines.
- The right-hand grip rule determines magnetic-field direction.
- Thumb points in the direction of conventional current.
- Curled fingers point in the magnetic-field direction.
- Current out of the page produces a counterclockwise field.
- Current into the page produces a clockwise field.
- Reversing current reverses the magnetic-field direction.
- For a long straight wire, B = μ₀I/(2πr).
- Increasing current strengthens the magnetic field.
- Increasing distance from the wire weakens the field.
- A current loop produces a magnetic field through its centre.
- Multiple loops combine their magnetic fields.
- A solenoid produces a field similar to a bar magnet.
- A solenoid has north and south poles.
- Increasing current or turns per unit length strengthens a solenoid's field.
- A ferromagnetic core can greatly strengthen the field of a coil.
- Current-carrying wires can exert magnetic forces on one another.
- Controlled magnetic fields from electric currents are fundamental to electromagnets, motors, speakers, relays, transformers and many other technologies.
Check Your Understanding
- What happens around a wire when electric current flows through it?
- Describe Oersted's discovery.
- Why was Oersted's experiment important to physics?
- Describe the magnetic-field pattern around a straight current-carrying wire.
- State the right-hand grip rule.
- What does the thumb represent in the right-hand grip rule?
- What do the curled fingers represent?
- What magnetic-field direction is produced by current coming out of the page?
- What magnetic-field direction is produced by current going into the page?
- What happens to the magnetic-field direction if the current is reversed?
- State the equation for magnetic flux density around a long straight wire.
- How does increasing current affect magnetic-field strength?
- How does increasing distance from the wire affect magnetic-field strength?
- A wire carries 4.0 A. Calculate the magnetic flux density 0.050 m from the wire using μ₀ = 4π × 10⁻⁷ T·m/A.
- Describe the magnetic-field pattern produced by a current loop.
- Explain why a solenoid produces a stronger and more organized field than a single loop.
- Compare the magnetic field of a solenoid with that of a permanent bar magnet.
- Explain how adding a soft iron core affects the magnetic field of a solenoid.
- Two parallel wires carry currents in the same direction. Describe the force between them.
- Explain how Oersted's discovery connects the study of electricity with the study of magnetism.