Physics notes, chapter 4

Electromagnetism

Textbook Physics Form 5 (DLP), pages 134–171

What this chapter covers

Explain the force on a current-carrying conductor in a magnetic field, the catapult field and Fleming's left-hand rule (4.1.1, 4.1.2)
Describe the factors that affect the magnitude of the force and the turning effect of a current-carrying coil (4.1.3, 4.1.4)
Explain how a direct current motor works and what affects its speed; compare brushed and brushless motors (4.1.5, 4.1.6)
Explain electromagnetic induction and the factors affecting the induced e.m.f.; state Faraday's law (4.2.1, 4.2.2)
Use Fleming's right-hand rule and Lenz's law to find the direction of induced current (4.2.3)
Compare direct current and alternating current generators (4.2.4)
Explain how a transformer works and solve problems on ideal transformers and efficiency (4.3.1, 4.3.2)
Explain energy loss in transformers, and the role of transformers in transmission and distribution of electricity (4.3.3, 4.3.4)

4.1Force on a current-carrying conductor in a magnetic field

A catapult field is the resultant magnetic field produced by the interaction between the magnetic field of a current-carrying conductor and the magnetic field of a permanent magnet. It exerts a force on the conductor.

When a current-carrying conductor is placed in a magnetic field it experiences a force. The direction of the force depends on the direction of the current and the direction of the magnetic field.

Magnetic field of a magnet and of a wire combine to form a catapult field, with a force on the wire — The two fields combine. The field lines are crowded (strong field) on one side of the wire and thin (weak field) on the other, so the wire is pushed towards the weak side. (Textbook Figure 4.3, p. 138)

Figure: Physics Form 5 (DLP) textbook, Figure 4.3, p. 138.

Fleming's left-hand rule

Finger	Shows
First (index) finger	Direction of the magnetic field, from north to south
Second (middle) finger	Direction of the electric current
Thumb	Direction of the force, and so the motion of the conductor

Left hand with thumb up for force, forefinger for magnetic field and middle finger for current — Fleming's left-hand rule. (Textbook Figure 4.4, p. 139)

Figure: Physics Form 5 (DLP) textbook, Figure 4.4, p. 139.

Hold the three fingers at right angles to each other. Use the left hand for a motor (current and field are given, find the force).

Magnitude of the force

The force increases when the current increases and when the strength of the magnetic field increases (for example by using stronger magnets or bringing the poles closer). In the textbook experiment the force shows up as a larger reading on an electronic balance.

Worked example

A wire between the poles of a magnet carries a current into the plane of the paper. The field points from N (left) to S (right). Find the direction of the force.

Index finger to the right (N to S), middle finger into the page. The thumb points downwards. If the current is reversed (out of the page) the force is upwards.

Current-carrying coil and the d.c. motor

A coil in a magnetic field has forces of equal size but opposite direction on its two opposite sides. This pair of forces gives a turning effect and the coil rotates about its axis. This is the working principle of the direct current (d.c.) motor, which changes electrical energy to kinetic energy.

Direct current motor in the first half and second half of one rotation — A d.c. motor. After half a turn the commutator halves swap brushes, so the current in the coil reverses and the coil keeps turning the same way. (Textbook Figure 4.13, p. 144)

Figure: Physics Form 5 (DLP) textbook, Figure 4.13, p. 144.

The commutator is a split ring that rotates with the coil. It reverses the direction of the current in the coil every half rotation, so the turning effect is always in the same direction. The carbon brushes stay fixed and touch the commutator.

The speed of rotation of a motor increases when the current in the coil increases, the magnetic field is stronger, or the coil has more turns.

Brushed and brushless motors

	Brushed motor	Brushless motor
Rotating part	Coil rotates, magnet stationary	Magnet rotates, coil stationary
Brushes and commutator	Carbon brushes wear out through friction	None, so no friction
Sparking	Sparks at commutator	No sparking
Noise	Louder	Quieter

In a motor, the commutator keeps the turning effect in one direction. It does not turn a.c. into d.c.; the supply is already d.c., and the commutator reverses the current in the coil.

A motor spins too slowly. State two changes that would make it spin faster.

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Increase the current (higher voltage); use stronger magnets; add more turns to the coil (any two).

4.2Electromagnetic induction

Electromagnetic induction is the production of an induced e.m.f. in a conductor when there is relative motion between the conductor and a magnetic field, or when the conductor is in a changing magnetic field. If the circuit is complete, an induced current flows.

The conductor must cut magnetic field lines (magnetic flux). A galvanometer deflects only while there is relative motion. If the magnet and the conductor are stationary, or move together with the same velocity, there is no induction.

Factors affecting the induced e.m.f.

The speed of relative motion between magnet and conductor.
The strength of the magnetic field.
The number of turns of the solenoid.

Faraday's law: the magnitude of the induced e.m.f. is directly proportional to the rate of cutting of magnetic flux.

Direction of the induced current

Straight wire: Fleming's right-hand rule. Thumb for the motion of the wire, first finger for the magnetic field, second finger for the induced current. Use the right hand for a generator.

Solenoid: Lenz's law. The induced current flows in a direction that opposes the change of magnetic flux that causes it.

Magnet movement	Pole induced at the nearer end of the solenoid	Effect
N pole pushed in	North	Repels the magnet
N pole pulled out	South	Attracts the magnet
S pole pushed in	South	Repels the magnet
S pole pulled out	North	Attracts the magnet

Four diagrams showing the pole induced in a solenoid when a bar magnet is pushed in or pulled out — Lenz's law: the solenoid always opposes the motion of the magnet. (Textbook Figure 4.28, p. 159)

Figure: Physics Form 5 (DLP) textbook, Figure 4.28, p. 159.

Lenz's law is conservation of energy in action. Work must be done to push the magnet against the repulsion, and that work becomes electrical energy.

Generators

	d.c. generator	a.c. generator
Coil ends connected to	Split-ring commutator	Two slip rings
Output	Direct current	Alternating current
Both	Coil is turned by an external force, cuts magnetic flux, e.m.f. is induced

A faster rotation cuts flux at a greater rate, so the induced e.m.f. is larger (Faraday's law).

Motor: left hand, current in, motion out. Generator: right hand, motion in, current out.

The north pole of a bar magnet is pulled away from a solenoid. What pole forms at the end of the solenoid nearest the magnet?

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A south pole. By Lenz's law it attracts the magnet to oppose its removal.

4.3Transformers

A transformer changes the value of an alternating voltage. It works only with a.c. because only a changing current makes a changing magnetic field in the core.

A simple transformer with primary coil, secondary coil and a laminated soft iron core — Structure of a simple transformer. (Textbook Figure 4.32, p. 163)

Figure: Physics Form 5 (DLP) textbook, Figure 4.32, p. 163.

Working principle. The a.c. in the primary coil produces a magnetic field that changes in size and direction. The soft iron core links this flux to the secondary coil. The changing flux induces an alternating voltage across the secondary coil.

Transformer equation: V_S / V_P = N_S / N_P
Step-up: N_S > N_P, so V_S > V_P. Step-down: N_S < N_P, so V_S < V_P.

Ideal transformer and efficiency

Efficiency = (output power / input power) × 100% = (V_SI_S / V_PI_P) × 100%. An ideal transformer has 100% efficiency, so V_PI_P = V_SI_S.

Worked example

An ideal transformer takes 240 V and gives 18 V to a 27 W device. The secondary coil has 60 turns. Find N_P, I_S and I_P.

N_P = 240 / 18 × 60 = 800 turns. I_S = 27 / 18 = 1.5 A. I_P = 27 / 240 = 0.1125 A.

Energy loss and how to reduce it

Cause of loss	Way to reduce it
Resistance of the coils (heating)	Use thicker copper wire
Eddy currents in the core	Use a laminated core of thin insulated sheets
Hysteresis (repeated magnetising)	Use soft iron for the core
Leakage of magnetic flux	Wind the secondary coil on top of the primary coil

Eddy currents are useful in an induction cooker: a high-frequency changing field induces eddy currents in the base of the pan, which heats it.

Transmission of electricity

Power station, step-up transformer, transmission lines at 275 kV and step-down transformers to homes — A step-up transformer raises the voltage for transmission; step-down transformers lower it in stages for consumers. (Textbook Figure 4.37, p. 167)

Figure: Physics Form 5 (DLP) textbook, Figure 4.37, p. 167.

High voltage means small current for the same power, so less energy is lost as heat in the cables (P = I²R).

In the figure, the step-up transformer (labelled N in the book) is at the power station, before transmission; step-down transformers (labelled T) are at the substations. Uses: microwave oven and X-ray machine use step-up; phone charger uses step-down.

Voltage goes up in a step-up transformer but the current goes down. A transformer never increases the power.

A transformer has 1 000 turns in the primary coil and 50 in the secondary. The input is 240 V. What is the output voltage?

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V_S = 240 × 50 / 1000 = 12 V (step-down).