This note covers how a changing magnetic field produces a voltage (electromagnetic induction), how an a.c. generator works, how a current in a magnetic field gives a force (the motor effect), and how transformers change voltage. These ideas explain how electricity is generated, moved around the country and used.
Key ideas
Electromagnetic induction. When a wire moves across a magnetic field, or the magnetic field around a wire changes, an e.m.f. is induced in the wire. If the wire is part of a complete circuit, a current flows.
- The wire must cut the field lines. Moving parallel to the field lines gives no e.m.f.
- A magnet pushed into a coil induces an e.m.f. while it is moving. If it stops, the e.m.f. falls to zero.
- Pulling the magnet out instead of pushing it in reverses the direction of the induced e.m.f.
- The induced e.m.f. is larger if the magnet moves faster, if the magnet is stronger, or if the coil has more turns.
- (Extended) The induced current flows in a direction that opposes the change that produced it. This is why you have to do work to push a magnet into a coil that is part of a circuit.
The a.c. generator. A coil is rotated between the poles of a magnet. The coil cuts field lines, so an e.m.f. is induced. The connection is made to the outside circuit through slip rings and carbon brushes.
- The e.m.f. is alternating: it changes direction every half turn. The graph of e.m.f. against time is a repeating wave shape.
- It is greatest when the coil moves at right angles to the field lines, and zero when it moves along them.
- Turning the coil faster gives a higher peak e.m.f. and a higher frequency, so the waves are taller and closer together.
Magnetic field of a current. A current in a straight wire is surrounded by circular magnetic field lines. A coil of wire (a solenoid) has a field like a bar magnet. The field is stronger with a larger current, more turns, or an iron core.
The motor effect. A wire carrying current in a magnetic field feels a force. The force is greatest when the wire is at right angles to the field, and is zero if the wire is parallel to it.
- The force reverses if the current is reversed or if the field is reversed.
- The force is larger with a larger current or a stronger magnetic field.
- (Extended) The direction is found with Fleming's left-hand rule: first finger points along the field, second finger along the current, and the thumb shows the direction of the force.
The d.c. motor. A rectangular coil sits in a magnetic field. The current is in opposite directions on the two sides, so the forces are opposite and the coil turns. A split-ring commutator reverses the current every half turn so the coil keeps turning in the same direction. A motor turns faster with a larger current, a stronger field or more turns on the coil.
Transformers. A transformer has two coils, the primary and the secondary, wound on a soft-iron core. An alternating current in the primary produces a changing magnetic field in the core. This field passes through the secondary and induces an alternating e.m.f. in it.
- A step-up transformer has more turns on the secondary and increases the voltage.
- A step-down transformer has fewer turns on the secondary and decreases the voltage.
- Transformers only work with alternating current. A steady direct current gives a constant field and so no induction.
- (Extended) For a transformer that is 100% efficient, the power in equals the power out.
Power transmission. Power stations transmit electricity at very high voltage, using step-up transformers. For the same power, a higher voltage means a smaller current. (Extended) The power wasted as heat in the cables is I²R, so a smaller current means much less energy is lost. Step-down transformers then reduce the voltage near homes.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Vp ÷ Vs = Np ÷ Ns | Transformer equation (extended). V is the p.d. across the coil and N is its number of turns. p = primary, s = secondary. |
| IpVp = IsVs | Power in = power out for a 100% efficient transformer (extended). |
| P = I²R | Power lost as heat in a cable of resistance R carrying current I (extended). |
| Induced e.m.f. | Voltage produced when a conductor cuts magnetic field lines, or the field through a coil changes. |
| Commutator | Split ring that reverses the current in a d.c. motor every half turn. |
| Slip rings | Continuous rings that connect a rotating coil to the outside circuit in an a.c. generator. |
Worked examples
Example 1 (extended) A transformer has 500 turns on its primary coil and is connected to the 230 V mains. The secondary must give 12 V. How many turns are needed on the secondary?
Use Vp ÷ Vs = Np ÷ Ns.
Rearrange: Ns = Np × Vs ÷ Vp = 500 × 12 ÷ 230 = 26.1.
Turns must be a whole number, so use 26.
Answer: 26 turns (a step-down transformer)
Example 2 (extended) The transformer in Example 1 is 100% efficient and the 12 V secondary supplies a current of 3.0 A. What current flows in the primary?
Power out = IsVs = 3.0 × 12 = 36 W.
Power in is also 36 W, so Ip = 36 ÷ 230 = 0.157 A.
Answer: 0.157 A
Example 3 (extended) A power station sends 5.0 MW along cables of total resistance 10 Ω. Compare the power lost as heat if the power is transmitted at 25 kV and at 250 kV.
Power = 5.0 × 106 W. Use I = P ÷ V.
At 25 kV: I = 5.0 × 106 ÷ 25 000 = 200 A. Power lost = I²R = 200² × 10 = 400 000 W = 400 kW.
At 250 kV: I = 5.0 × 106 ÷ 250 000 = 20 A. Power lost = 20² × 10 = 4000 W = 4.0 kW.
Answer: 400 kW at 25 kV and 4.0 kW at 250 kV. Ten times the voltage gives one hundredth of the loss.
Common errors
- Saying a stationary magnet inside a coil induces a current. There must be relative movement or a changing field.
- Saying a transformer works with a battery. It needs an alternating current to make a changing field.
- Mixing up Np and Ns in the transformer equation. A step-up transformer has more turns on the secondary.
- Saying a step-up transformer gives you more power. Power out cannot be greater than power in.
- Using the left-hand rule for induction. Fleming's left-hand rule gives the force on a current-carrying wire. It is not used here to find the direction of an induced current.
Exam tip: To explain why high-voltage transmission saves energy, state the chain in order: higher voltage, smaller current for the same power, less heating (I²R) in the cables.
Check yourself
- Give two ways of increasing the e.m.f. induced when a magnet is pushed into a coil.
Answer
Any two of: move the magnet faster, use a stronger magnet, use a coil with more turns. - (Extended) A transformer has 240 turns on the primary and is connected to 230 V. The secondary gives 46 V. How many turns does the secondary have?
Answer
Ns = 240 × 46 ÷ 230 = 48 turns. - How can the direction of the force on a wire carrying current in a magnetic field be reversed?
Answer
Reverse the current, or reverse the magnetic field (swap the magnet poles). Doing both together leaves the force unchanged. - An a.c. generator coil is turned twice as fast. State two changes to the e.m.f. output.
Answer
The peak e.m.f. is larger and the frequency is higher, so more cycles occur each second.