Electromagnetism
3. Electromagnetic Force
Learning outcomes
- I can explain how magnetic fields and currents interact.
- I can describe electromagnetic forces in practical systems.
- I can analyze the operation of devices that use electromagnetic forces.
- I can identify factors affecting electromagnetic force.
- I can solve problems involving electromagnetic interactions.
Electromagnetic Force
How Magnetic Fields and Currents Interact
When an electric current flows through a conductor, it produces a magnetic field around the conductor. If that conductor is placed in another magnetic field, the two magnetic fields interact.
This interaction can produce a force on the conductor.
This is called the motor effect and is one of the most important applications of electromagnetism:
current + magnetic field → force
For a straight current-carrying conductor:
F = BIL sin θ
where:
- F = electromagnetic force (N)
- B = magnetic flux density (T)
- I = current (A)
- L = length of conductor within the magnetic field (m)
- θ = angle between the current and magnetic field
The Motor Effect
A current-carrying wire produces its own magnetic field.
When the wire is placed inside an external magnetic field, the fields interact.
On one side of the wire, the fields may reinforce each other.
On the other side, they may partially oppose each other.
The resulting field pattern is asymmetric and the conductor experiences a net force.
This is the basis of the:
motor effect
Force on the Moving Charges
Electric current consists of moving charge.
Individual moving charges in a magnetic field experience:
F = |q|vB sin θ
where:
- |q| = charge magnitude
- v = charge velocity
- B = magnetic flux density
- θ = angle between v and B
The magnetic forces acting on the moving charges are transferred to the conductor.
At the macroscopic level, this gives:
F = BIL sin θ
for a straight conductor.
Maximum Electromagnetic Force
If the conductor is perpendicular to the magnetic field:
θ = 90°
Since:
sin 90° = 1
the equation becomes:
F = BIL
The force is maximum.
Therefore:
current perpendicular to field → maximum force
Zero Electromagnetic Force
If the conductor is parallel to the magnetic field:
θ = 0°
Since:
sin 0° = 0
then:
F = 0
Therefore:
current parallel to field → no magnetic force
This angular dependence is important when analyzing motors and other electromagnetic devices.
Effect of Angle
In general:
F = BIL sin θ
Therefore:
| θ | sin θ | Force |
|---|---|---|
| 0° | 0 | Zero |
| 30° | 0.50 | Half maximum |
| 45° | 0.707 | 70.7% maximum |
| 60° | 0.866 | 86.6% maximum |
| 90° | 1 | Maximum |
The force depends on the component of the magnetic field perpendicular to the current.
Direction of the Force
The electromagnetic force acts perpendicular to both:
- current direction
- magnetic-field direction
For conventional current, the direction can be determined using:
Fleming's Left-Hand Rule
Fleming's Left-Hand Rule
Hold your left:
- thumb
- first finger
- second finger
at right angles to one another.
First finger
Points in the direction of the magnetic:
Field
Second finger
Points in the direction of conventional:
Current
Thumb
Points in the direction of:
Force or Motion
A useful memory aid is:
First = Field
seCond = Current
thuMb = Motion
Conventional Current
Fleming's Left-Hand Rule uses:
conventional current
Conventional current is defined as the direction positive charge would move.
In a metal conductor, electrons actually drift in the opposite direction.
Unless specifically told otherwise, use:
conventional current direction
when applying the rule.
Reversing the Current
Suppose a conductor experiences a force upward.
If the current is reversed while the magnetic field remains unchanged:
force direction reverses
Therefore:
upward → downward
This is important in devices where the direction of motion must be controlled.
Reversing the Magnetic Field
If the magnetic-field direction is reversed while current remains unchanged:
force direction reverses
Again:
upward → downward
Reversing Both
If both:
- current direction
- magnetic-field direction
are reversed simultaneously, the force direction remains unchanged.
This is because each reversal individually reverses the force, producing two reversals overall.
Factors Affecting Electromagnetic Force
From:
F = BIL sin θ
four main factors affect force.
Magnetic flux density
B ↑ → F ↑
A stronger magnetic field produces a larger force.
Current
I ↑ → F ↑
A larger current produces a larger force.
Length in the field
L ↑ → F ↑
A longer section of conductor inside the field produces a larger force.
Angle
Force depends on:
sin θ
Maximum at 90°.
Zero at 0° or 180°.
Example: Calculating Force
A wire carries:
I = 4.0 A
through a magnetic field:
B = 0.50 T
The length of wire inside the field is:
L = 0.30 m
The wire is perpendicular to the field.
Use:
F = BIL
F = (0.50)(4.0)(0.30)
F = 0.60 N
Example: Force at an Angle
A conductor has:
B = 0.80 T
I = 3.0 A
L = 0.40 m
θ = 30°
Use:
F = BIL sin θ
F = (0.80)(3.0)(0.40)(sin 30°)
F = (0.80)(3.0)(0.40)(0.50)
F = 0.48 N
Example: Finding Current
A wire experiences a force:
F = 1.2 N
in a field:
B = 0.50 T
The length in the field is:
L = 0.80 m
The conductor is perpendicular to the field.
Use:
F = BIL
Rearrange:
I = F/(BL)
I = 1.2/[(0.50)(0.80)]
I = 1.2/0.40
I = 3.0 A
Example: Finding Magnetic Flux Density
A conductor experiences:
F = 0.36 N
when carrying:
I = 2.0 A
The length inside the field is:
L = 0.30 m
The wire is perpendicular to the field.
Use:
B = F/(IL)
B = 0.36/[(2.0)(0.30)]
B = 0.60 T
Example: Unit Conversion
A 12 cm wire carries 5.0 A perpendicular to a 0.40 T magnetic field.
First convert:
12 cm = 0.12 m
Then:
F = BIL
F = (0.40)(5.0)(0.12)
F = 0.24 N
Always convert length to metres before using the equation.
Forces on Parallel Current-Carrying Wires
Two current-carrying wires can exert forces on each other.
Each wire produces a magnetic field.
The other wire lies inside that field and therefore experiences a magnetic force.
For parallel wires:
currents in the same direction → attraction
currents in opposite directions → repulsion
Why Parallel Currents Attract
Consider two parallel wires carrying current in the same direction.
Wire A produces a magnetic field at Wire B.
Wire B carries current inside this field and experiences a force toward Wire A.
Similarly, Wire B produces a field that causes Wire A to experience a force toward Wire B.
Therefore:
the wires attract
Why Opposite Currents Repel
If the currents flow in opposite directions, the magnetic force directions reverse.
Each wire is pushed away from the other.
Therefore:
opposite parallel currents repel
This is a direct consequence of current-produced magnetic fields interacting with other currents.
Force Between Long Parallel Wires
For two long parallel wires separated by distance r:
F/L = μ₀I₁I₂/(2πr)
where:
- F/L = force per unit length (N/m)
- μ₀ = permeability of free space
- I₁ = current in first wire
- I₂ = current in second wire
- r = separation between wires
This equation shows:
larger currents → larger force
greater separation → smaller force
Current-Carrying Coils
A coil placed in a magnetic field can experience forces on different sections.
Opposite sides of the coil carry current in opposite directions.
Therefore, the forces on those sides also point in opposite directions.
Rather than simply moving the entire coil sideways, these forces can create:
torque
or a turning effect.
Torque on a Coil
For an ideal coil:
τ = NBIA sin θ
where:
- τ = torque (N·m)
- N = number of turns
- B = magnetic flux density (T)
- I = current (A)
- A = coil area (m²)
- θ = angle between the coil's magnetic moment and B
This equation shows that torque can be increased by increasing:
- number of turns
- magnetic-field strength
- current
- coil area
Electromagnetic Force in Motors
An electric motor converts:
electrical energy → mechanical energy
The basic process is:
current flows through coil
↓
coil lies in magnetic field
↓
opposite sides experience opposite forces
↓
forces create torque
↓
rotor turns
Why a Motor Rotates
Consider a rectangular coil between magnetic poles.
On one side of the coil, current may flow into the page.
On the opposite side, current flows out of the page.
Using Fleming's Left-Hand Rule:
- one side experiences an upward force
- the other experiences a downward force
These forces form a couple.
The resulting torque rotates the coil.
The Split-Ring Commutator
In a simple DC motor, the current must reverse approximately every half-turn so that the torque continues in the same overall rotational direction.
The:
split-ring commutator
performs this function.
It reverses current through the coil as the motor rotates.
Therefore, the magnetic forces reverse at the correct time and continuous rotation can occur.
Increasing Motor Force and Torque
A motor can produce greater electromagnetic force by increasing:
- B
- I
- effective conductor length
Motor torque can also be increased by:
- increasing number of coil turns
- increasing coil area
- optimizing coil orientation
Engineering involves balancing these improvements against:
- heating
- size
- mass
- electrical power
- material limitations
Electromagnetic Force in Loudspeakers
A loudspeaker also uses the motor effect.
A voice coil sits inside the field of a permanent magnet.
An audio current passes through the coil.
The coil experiences an electromagnetic force.
How a Loudspeaker Produces Sound
The audio current continually changes.
When current flows one way:
force acts one way
When current reverses:
force reverses
Therefore, the voice coil moves back and forth.
The voice coil is attached to the speaker cone.
So:
electrical signal
↓
changing current
↓
changing electromagnetic force
↓
voice coil vibrates
↓
cone vibrates
↓
air pressure changes
↓
sound wave
Force and Speaker Volume
For the simplified relationship:
F = BIL
increasing current increases force.
A larger varying current can therefore produce larger cone movements, within the speaker's operating limits.
Larger vibration amplitude generally produces a sound wave with greater amplitude.
This is associated with increased:
sound intensity and perceived loudness
Electromagnetic Relays
A relay uses electromagnetic forces differently.
Current flows through a coil.
The coil produces a magnetic field.
The field magnetizes or attracts a ferromagnetic armature.
The armature moves and changes the position of electrical contacts.
Therefore:
electrical signal → magnetic field → mechanical movement → switching
Solenoid Actuators
A solenoid actuator converts electrical energy into approximately linear motion.
When current flows through a coil:
- a magnetic field is produced
- a ferromagnetic plunger experiences a force
- the plunger moves
These devices are used in:
- valves
- door locks
- vehicle systems
- vending machines
- industrial machines
- robotic systems
Moving-Coil Meters
A moving-coil meter places a current-carrying coil in a magnetic field.
The electromagnetic forces produce torque.
Greater current produces greater torque.
The coil rotates against a restoring mechanism.
A pointer attached to the coil can therefore indicate the current or another electrical quantity.
This principle is used in traditional:
- galvanometers
- ammeters
- voltmeters
Electromagnetic Force in Particle Beams
The same magnetic-force principle applies to moving individual charges.
For a particle:
F = |q|vB sin θ
A magnetic field can therefore:
- bend particle beams
- guide charged particles
- produce circular motion
- help confine plasma
This is used in:
- particle accelerators
- mass spectrometers
- fusion research
- particle detectors
Macroscopic and Microscopic Views
There are two useful ways to understand electromagnetic force.
Microscopic view
Moving individual charges experience:
F = |q|vB sin θ
Macroscopic view
A current-carrying conductor experiences:
F = BIL sin θ
The macroscopic motor effect ultimately results from magnetic forces acting on moving charges inside the conductor.
Magnetic Force Does Not Create Energy
A magnetic field can exert forces and redirect moving charges, but it does not create energy.
In motors, the energy ultimately comes from the:
electrical power supply
The magnetic field provides a mechanism that allows electrical energy to be converted into mechanical motion.
Therefore:
magnetic interaction enables energy conversion
rather than generating energy from nothing.
Power in an Electromechanical Device
Electrical input power can be calculated using:
P = VI
A motor converts part of this electrical power into useful mechanical power.
However, some energy is dissipated through:
- resistance heating
- friction
- sound
- magnetic losses
Therefore:
P_input = P_useful + P_losses
Efficiency
Motor efficiency can be calculated using:
efficiency = useful output power / input power
or:
efficiency (%) = (useful output power / input power) × 100
For example, if a motor receives:
P_input = 500 W
and produces:
P_useful = 400 W
then:
efficiency = 400/500 × 100
efficiency = 80%
The remaining 20% is transferred into less useful forms such as heat and sound.
Example: Motor Force
A motor conductor has:
B = 0.75 T
I = 6.0 A
L = 0.20 m
The conductor is perpendicular to the field.
F = BIL
F = (0.75)(6.0)(0.20)
F = 0.90 N
If the motor contains many conductor sections experiencing similar forces, their combined effects can produce substantial torque.
Example: Effect of Doubling Current
A conductor initially experiences:
F = 0.40 N
The current is doubled while B, L and θ remain unchanged.
Since:
F ∝ I
the new force is:
F = 0.80 N
Example: Effect of Doubling Field Strength
A wire experiences:
F = 0.25 N
The magnetic flux density doubles.
Since:
F ∝ B
the new force is:
F = 0.50 N
Example: Changing Several Variables
A conductor initially experiences force F.
The current doubles:
I → 2I
The magnetic flux density triples:
B → 3B
The length and angle remain unchanged.
Since:
F ∝ BI
the new force is:
(2)(3)F
Therefore:
F_new = 6F
Example: Force at 60°
A wire has:
B = 0.40 T
I = 5.0 A
L = 0.50 m
θ = 60°
Use:
F = BIL sin θ
F = (0.40)(5.0)(0.50)(sin 60°)
F = (1.0)(0.866)
F ≈ 0.87 N
If the conductor were perpendicular to the field, the force would be:
F = (0.40)(5.0)(0.50)
F = 1.0 N
The angled conductor therefore experiences a smaller force.
Example: Multi-Step Electromagnetic Problem
A 25 cm conductor carries 8.0 A in a 0.60 T magnetic field at 30°.
Step 1: Convert length
25 cm = 0.25 m
Step 2: Select equation
F = BIL sin θ
Step 3: Substitute
F = (0.60)(8.0)(0.25)(sin 30°)
F = (0.60)(8.0)(0.25)(0.50)
F = 0.60 N
If the current is reversed, the magnitude remains:
0.60 N
but the force direction reverses.
Analyzing Electromagnetic Devices
When analyzing a device that uses electromagnetic force, ask:
Where does the current flow?
Identify the current-carrying conductor or coil.
Where is the magnetic field?
Identify the permanent magnet, electromagnet or other field source.
What is the angle between I and B?
This determines the force magnitude.
What is the force direction?
Use Fleming's Left-Hand Rule.
What does the force do?
It may produce:
- rotation
- vibration
- linear movement
- switching
- beam deflection
Where does the energy come from?
Usually from an electrical power source.
Comparing Devices
| Device | Current-Carrying Part | Magnetic Interaction Produces |
|---|---|---|
| Electric motor | Coil/winding | Rotation |
| Loudspeaker | Voice coil | Vibration |
| Moving-coil meter | Coil | Pointer rotation |
| Solenoid actuator | Coil/core system | Linear movement |
| Relay | Electromagnetic coil | Switching |
| Particle accelerator | Moving charged particles | Beam deflection |
The applications differ, but the underlying electromagnetic principles are closely related.
Common Mistakes
Mistake: Saying the force is always F = BIL.
This simplified equation applies when current is perpendicular to the magnetic field. In general, use F = BIL sin θ.
Mistake: Using centimetres directly for L.
Convert length to metres.
Mistake: Saying current parallel to the magnetic field experiences maximum force.
Parallel current produces zero magnetic force.
Mistake: Using the right-hand grip rule to find motor force direction.
For conventional current in motor-effect problems, use Fleming's Left-Hand Rule.
Mistake: Forgetting that reversing current reverses the force.
Mistake: Forgetting that reversing the magnetic field also reverses the force.
Mistake: Saying parallel currents in the same direction repel.
They attract.
Mistake: Saying opposite parallel currents attract.
They repel.
Mistake: Saying a magnetic field supplies the energy used by a motor.
The motor's energy comes from its electrical supply.
Mistake: Confusing force and torque.
Forces acting at suitable positions can produce torque.
Key Terms
Electromagnetic force — force associated with interactions between electric charges, currents, electric fields and magnetic fields.
Motor effect — force experienced by a current-carrying conductor placed in a magnetic field.
Magnetic flux density (B) — measure of magnetic-field strength and direction, measured in teslas.
Current (I) — rate of flow of electric charge.
Conductor — material through which electric charge can move.
Fleming's Left-Hand Rule — rule used to determine force direction on a current-carrying conductor in a magnetic field.
Conventional current — defined direction of positive-charge flow.
Torque — turning effect produced by a force.
Couple — pair of forces producing a turning effect.
Rotor — rotating part of an electric motor.
Voice coil — current-carrying coil in a loudspeaker that experiences electromagnetic force.
Solenoid actuator — device using electromagnetism to produce controlled linear movement.
Armature — movable magnetic component in an electromagnetic device.
Electromechanical device — device that converts between electrical and mechanical forms of energy or signals.
Key Takeaways
- Electric currents produce magnetic fields.
- A current-carrying conductor can experience a force in an external magnetic field.
- This interaction is called the motor effect.
- The general force equation is F = BIL sin θ.
- When the conductor is perpendicular to the field, F = BIL.
- Force is maximum when current and field are perpendicular.
- Force is zero when current and field are parallel.
- Increasing B increases electromagnetic force.
- Increasing I increases electromagnetic force.
- Increasing the conductor length within the field increases force.
- Fleming's Left-Hand Rule determines force direction for conventional current.
- Reversing current reverses force direction.
- Reversing the magnetic field reverses force direction.
- Reversing both current and field leaves the force direction unchanged.
- Parallel currents in the same direction attract.
- Parallel currents in opposite directions repel.
- Forces on a current-carrying coil can produce torque.
- Electric motors use electromagnetic force to produce rotation.
- Loudspeakers use electromagnetic force to produce vibration.
- Relays, solenoid actuators and moving-coil meters also use electromagnetic interactions.
- Electromagnetic forces provide an important mechanism for converting electrical energy into mechanical motion.
Check Your Understanding
- Explain what is meant by the motor effect.
- State the general equation for force on a straight current-carrying conductor in a magnetic field.
- What does each quantity in F = BIL sin θ represent?
- At what angle is electromagnetic force maximum?
- At what angle is electromagnetic force zero?
- State Fleming's Left-Hand Rule.
- What happens to force direction if current is reversed?
- What happens if the magnetic field is reversed?
- What happens if both current and magnetic-field directions are reversed?
- A 0.40 m wire carries 3.0 A perpendicular to a 0.50 T field. Calculate the force.
- A 20 cm wire carries 6.0 A perpendicular to a 0.80 T field. Calculate the force.
- A conductor carries 4.0 A through a 0.60 T field at 30°. Its length in the field is 0.50 m. Calculate the force.
- Explain how increasing current affects electromagnetic force.
- Explain how increasing magnetic flux density affects electromagnetic force.
- Describe the force between two parallel wires carrying currents in the same direction.
- Describe the force between two parallel wires carrying currents in opposite directions.
- Explain how electromagnetic forces produce torque in an electric motor.
- Explain how a loudspeaker uses electromagnetic force to produce sound.
- Compare the use of electromagnetic force in a motor, loudspeaker and solenoid actuator.
- A motor designer wants to increase the electromagnetic force without increasing the conductor length. Describe at least three changes that could be considered and explain the physics behind each.