P28: Electromagnets and the Motor Effect
Solenoids and electromagnets, the motor effect, Fleming's left-hand rule, the force on a current-carrying conductor, electric motors and loudspeakers.
Magnetic Fields from Currents
When a current flows through a wire, a magnetic field is produced around the wire. This is called the electromagnetic effect. The magnetic field forms concentric circles around the wire.
- Increasing the current increases the strength of the magnetic field
- The direction of the magnetic field depends on the direction of the current
- Use the right-hand grip rule to determine the field direction: point your thumb in the direction of the current and your fingers curl in the direction of the magnetic field
Solenoids
A solenoid is a long coil of wire that produces a strong, uniform magnetic field inside it when a current flows. The field outside the solenoid is similar to that of a bar magnet.
- Inside the solenoid, the field lines are parallel and close together, showing a strong uniform field
- Outside, the field lines curve from one end (north pole) to the other (south pole)
- The strength of the solenoid's magnetic field can be increased by: increasing the current, increasing the number of turns on the coil, or using a soft iron core inside the solenoid
A solenoid with an iron core becomes an electromagnet. Adding an iron core makes the magnetic field much stronger because iron is easily magnetised.
Electromagnets
An electromagnet is a solenoid with a soft iron core. It can be switched on and off by controlling the current. Electromagnets are used in many applications because their magnetic field can be controlled.
Factors Affecting Electromagnet Strength
- Increasing the current makes the electromagnet stronger
- Increasing the number of turns on the coil makes the electromagnet stronger
- Using a soft iron core (instead of no core) makes the electromagnet much stronger
- Using a hard magnetic core would retain magnetism after the current is switched off, which is undesirable for an electromagnet
Uses of Electromagnets
- Cranes in scrap yards to lift and sort magnetic metals
- Electric bells and relay switches
- Magnetic separators in recycling
- MRI scanners in hospitals
- Circuit breakers for safety
The Motor Effect
The motor effect is the force experienced by a current-carrying conductor placed in a magnetic field. The force is greatest when the conductor is perpendicular to the magnetic field lines, and zero when the conductor is parallel to the field.
- A wire carrying a current in a magnetic field experiences a force
- The force pushes the wire at right angles to both the current direction and the magnetic field direction
- If the wire is parallel to the magnetic field, there is no force
- Reversing the current direction reverses the force direction
- Reversing the magnetic field direction reverses the force direction
Fleming's Left-Hand Rule
Fleming's left-hand rule is used to determine the direction of the force (motion) on a current-carrying wire in a magnetic field.
- First finger points in the direction of the magnetic Field (from north to south)
- Second finger points in the direction of the Current (conventional current, positive to negative)
- Thumb points in the direction of the Motion (force)
Hold your left hand with the first three fingers at right angles to each other. This only works for the motor effect (where a current causes a force).
Remember: FBI = First finger (Field), seCond finger (Current), thuMb (Motion). Use your LEFT hand for the motor effect.
Force on a Current-Carrying Conductor
Force Equation
F = B I l
F = force on the conductor (N)
B = magnetic flux density (T, tesla)
I = current in the conductor (A)
l = length of conductor in the magnetic field (m)
This equation applies when the conductor is at right angles (90 degrees) to the magnetic field. If the conductor is at an angle to the field, the force is reduced. If the conductor is parallel to the field, the force is zero.
Worked Example 1
A wire of length 0.05 m carries a current of 4 A in a magnetic field of flux density 0.2 T. Calculate the force on the wire.
Solution:
F = B I l
F = 0.2 x 4 x 0.05
F = 0.04 N
Worked Example 2
A wire carrying a current of 3 A is placed perpendicular to a magnetic field of flux density 0.5 T. The wire experiences a force of 0.15 N. Calculate the length of wire in the field.
Solution:
F = B I l, so l = F / (B x I)
l = 0.15 / (0.5 x 3)
l = 0.15 / 1.5 = 0.1 m
The Electric Motor
An electric motor uses the motor effect to produce a continuous rotational force. A current-carrying coil in a magnetic field experiences forces that cause it to rotate.
- A rectangular coil of wire sits between the poles of a permanent magnet
- Current flows through the coil and the forces on each side of the coil create a turning effect (a couple)
- The coil rotates, but without a commutator it would stop at the vertical position
- A split-ring commutator reverses the direction of current every half turn, keeping the coil rotating in the same direction
- The direction of rotation can be reversed by reversing the current or the magnetic field
- The speed can be increased by increasing the current
Loudspeakers
A loudspeaker converts electrical signals into sound waves using the motor effect. A current-carrying coil in a magnetic field experiences a force that makes it vibrate.
- An alternating current flows through a coil attached to a cone
- The coil sits inside a permanent magnet
- As the current alternates, the force on the coil changes direction, causing the coil and cone to vibrate
- The vibrating cone produces sound waves at the same frequency as the alternating current
- Increasing the current amplitude increases the volume (louder sound)
- Changing the frequency of the current changes the pitch of the sound
Practice Questions
1. Describe how you would increase the strength of an electromagnet. [3 marks]
Increase the current flowing through the coil, increase the number of turns on the coil, or add a soft iron core inside the solenoid.
2. A wire of length 0.12 m carries a current of 2 A perpendicular to a magnetic field of flux density 0.3 T. Calculate the force on the wire. [2 marks]
F = B I l = 0.3 x 2 x 0.12 = 0.072 N
3. Use Fleming's left-hand rule to determine the direction of the force on a wire carrying a current into the page in a magnetic field pointing upwards. [2 marks]
Using Fleming's left-hand rule: first finger points up (field direction), second finger points into the page (current), thumb points to the left (force direction).
4. Explain the role of the split-ring commutator in an electric motor. [3 marks]
The split-ring commutator reverses the direction of current in the coil every half turn. This ensures the forces on the coil always act in the same rotational direction, so the coil continues to rotate rather than stopping at the vertical position.
5. Explain how a loudspeaker uses the motor effect to produce sound. [3 marks]
An alternating current flows through a coil in a magnetic field. The motor effect produces a force on the coil that changes direction as the current alternates. This causes the coil and attached cone to vibrate, producing sound waves at the frequency of the alternating current.
Maths Skills
F = BIl Calculations
Force on a Current-Carrying Conductor
F = B I l
F = force (N), B = magnetic flux density (T), I = current (A), l = length of wire in the field (m)
This equation applies when the wire is at 90° to the magnetic field.
Worked Example 1: Finding Force
A wire of length 8 cm carries a current of 5 A perpendicular to a magnetic field of flux density 0.3 T. Calculate the force.
l = 8 cm = 0.08 m (always convert to metres)
F = B I l = 0.3 × 5 × 0.08 = 0.12 N
Worked Example 2: Finding Magnetic Flux Density
A wire of length 0.04 m carries a current of 3 A perpendicular to a magnetic field. The force on the wire is 0.06 N. Calculate the magnetic flux density.
F = B I l, so B = F / (I × l)
B = 0.06 / (3 × 0.04) = 0.06 / 0.12 = 0.5 T
Fleming's Left-Hand Rule: Determining Direction
- First finger = direction of the magnetic Field (N to S)
- Second finger = direction of conventional Current (+ to –)
- Thumb = direction of the Motion (force)
- Use your LEFT hand only. The right hand is for the generator effect.
- If the current is reversed, the force reverses. If the field is reversed, the force reverses. If both are reversed, the force stays the same direction.
Applying Fleming's Left-Hand Rule
A wire carries a current vertically upwards. The magnetic field points from left to right. In which direction is the force?
First finger: points from left to right (field direction). Second finger: points upwards (current). Thumb: points out of the page (towards you). The force is out of the page.
Common Misconceptions
"The motor effect only works with permanent magnets." The motor effect works with any source of magnetic field, including electromagnets and solenoids. In fact, many motors and loudspeakers use electromagnets rather than permanent magnets because the field strength can be controlled by varying the current. The key requirement is a magnetic field and a current-carrying conductor at right angles to it — the source of the field does not matter.
"Increasing the current always increases the force on the wire." Increasing the current only increases the force if the magnetic field strength and the wire orientation remain the same. If the wire is not perpendicular to the field, the effective component of the field is reduced. If the wire is parallel to the field, the force is zero regardless of the current. The relationship F = BIl assumes the wire is at 90° to the field.
"Fleming's right-hand rule is the same as the left-hand rule but for the other hand." Fleming's left-hand rule is for the motor effect (where a current in a magnetic field produces a force). Fleming's right-hand rule is for the generator effect (where a conductor moving in a magnetic field induces a current). They are related but apply to different physical situations. Using the wrong hand will give the wrong answer.
6-Mark Extended Question
Explain how an electric motor works. Discuss how the design ensures continuous rotation. [6 marks]
An electric motor consists of a rectangular coil of wire placed between the poles of a permanent magnet (or electromagnet). When a current flows through the coil, each side of the coil that is perpendicular to the magnetic field experiences a force due to the motor effect (F = BIl). The forces on opposite sides of the coil are in opposite directions because the current flows in opposite directions on each side. This creates a pair of forces that form a couple, producing a rotational effect (torque) that causes the coil to rotate. However, without a commutator, the coil would only rotate to the vertical position and then stop, because at that point the forces act along the same line and produce no turning effect. To ensure continuous rotation, a split-ring commutator is used. The commutator is a ring split into two halves, with each half connected to one end of the coil. As the coil rotates past the vertical position, the commutator halves swap which brush they are in contact with. This reverses the direction of current through the coil every half turn. Because the current reverses just as the coil passes the vertical, the forces on the coil continue to push it in the same rotational direction. The motor therefore rotates continuously in one direction. The speed of rotation can be increased by increasing the current, and the direction of rotation can be reversed by reversing the polarity of the supply.
AO3: Analyse and Evaluate
A student investigates how the force on a current-carrying conductor depends on the current. They use a wire of length 5 cm in a magnetic field and vary the current. Their results are:
| Current (A) | Force (N) |
|---|---|
| 0.5 | 0.010 |
| 1.0 | 0.020 |
| 1.5 | 0.030 |
| 2.0 | 0.040 |
| 2.5 | 0.050 |
| 3.0 | 0.058 |
(a) Plot a graph of force against current and describe the relationship.
(b) The student expected a straight line through the origin. The value at 3.0 A is slightly lower than expected. Suggest a reason for this.
(c) Use the data from the first five points to calculate the magnetic flux density B. Then predict the force for a current of 4.0 A.
(a) The graph of force against current is a straight line passing through the origin for the first five points. This shows that force is directly proportional to current (F ∝ I), which is consistent with F = BIl where B and l are constant. The gradient is constant at 0.020 N/A.
(b) At 3.0 A, the force is 0.058 N instead of the expected 0.060 N. This could be because at higher currents the wire heats up, increasing its resistance. The increased resistance reduces the actual current flowing compared to the measured value, leading to a slightly lower force. Alternatively, the wire may have shifted slightly so it is no longer perfectly perpendicular to the field, reducing the effective force component.
(c) Using F = BIl: gradient = F/I = Bl, so B = gradient / l = 0.020 / 0.05 = 0.40 T.
For I = 4.0 A: F = BIl = 0.40 × 4.0 × 0.05 = 0.080 N (assuming the relationship remains linear and the wire stays perpendicular).
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