Electromagnetic Induction
This topic covers electromagnetic induction, the principle that a changing magnetic field or the motion of a wire through a magnetic field can generate a voltage. This is the fundamental concept behind electric generators and transformers.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- A voltage (e.m.f.) is induced in a conductor only when there is relative motion between the conductor and a magnetic field, or when the magnetic field passing through a coil changes in strength.
- The magnitude of the induced voltage is directly proportional to the rate at which magnetic field lines are cut. This rate can be increased by moving the wire/magnet faster, using a stronger magnet, or using a coil with more turns.
- The direction of the induced current creates a magnetic field that opposes the original change that caused it (Lenz's Law). This is a consequence of the conservation of energy.
- An AC generator rotates a coil in a constant magnetic field, causing the magnetic flux through the coil to change continuously. This produces a sinusoidal alternating voltage.
- The output voltage of an AC generator can be increased by: spinning the coil faster, using a stronger magnet, increasing the number of turns on the coil, or increasing the area of the coil.
- The graphical output of a simple AC generator is a sine wave. The amplitude (peak voltage) and frequency of this wave are both directly proportional to the speed of rotation.
› Why does this happen?
Where does the induced voltage come from?
A metal wire contains free-moving electrons. When the wire moves through a magnetic field, the field exerts a force on these moving electrons. This force pushes the free electrons towards one end of the wire, making it negatively charged. The other end, now with a shortage of electrons, is left with a net positive charge. This separation of charge creates a potential difference, or voltage, across the wire. If the wire is part of a complete circuit, this voltage drives an induced current.
Why does the induced current oppose the change (Lenz's Law)?
This is a direct result of the law of conservation of energy. Imagine pushing the north pole of a magnet into a coil. This induces a current. If this current created a south pole that *attracted* the magnet, the magnet would accelerate into the coil, inducing an even bigger current and a stronger attraction. You would get ever-increasing electrical energy for free, which is impossible. Therefore, the induced current *must* create a north pole to *repel* the incoming magnet. You have to do work to push the magnet in against this repulsion, and the work you do is converted into the electrical energy of the current.
Why is an AC generator's output a sine wave?
A voltage is induced because the sides of the spinning coil are cutting through magnetic field lines. The size of the voltage depends on how quickly the wire cuts these lines.
- Maximum voltage is induced when the sides of the coil are moving perpendicular to the magnetic field. At this point, they cut through the field lines at the fastest possible rate.
- Zero voltage is induced when the sides of the coil are, for an instant, moving parallel to the magnetic field. Here, they are not cutting any field lines at all.
As the coil rotates, its direction of motion continuously changes relative to the field, causing the rate of cutting to vary smoothly between maximum and zero. This produces the smooth, repeating shape of a sine wave.
Formulae
Induced Voltage ∝ Rate of change of magnetic flux This is the core conceptual relationship. Use it to determine how changes in speed, magnetic field strength, or coil properties affect the output voltage. For an AC generator, this means: Peak Voltage ∝ (Number of turns) × (Magnetic field strength) × (Area of coil) × (Frequency of rotation).
Definitions
- Electromagnetic Induction
- The production of a voltage (e.m.f.) across an electrical conductor in a changing magnetic field or due to the conductor's motion through a magnetic field.
- Lenz's Law
- States that the direction of the induced current is always such that it opposes the change in magnetic flux that caused it.
- AC Generator
- A device that converts mechanical rotational energy into alternating current (AC) electrical energy using the principle of electromagnetic induction.
Worked example
The graph shows the output voltage from a simple AC generator over time. At t=0, the coil is horizontal. The generator is then modified: the direction of the magnetic field is reversed, and the speed of rotation is halved. Which of the following graphs (A, B, C, D) represents the new output voltage? [Initial Graph: A sine wave starting at 0, reaching a peak of +2V at 0.25s, crossing zero at 0.5s, reaching a trough of -2V at 0.75s, and completing one cycle at 1.0s.] [Option A: A sine wave with peak voltage +1V and a period of 2.0s, starting at 0 and initially decreasing.] [Option B: A cosine wave with peak voltage +1V and a period of 2.0s, starting at +1V.] [Option C: A sine wave with peak voltage +1V and a period of 2.0s, starting at 0 and initially increasing.] [Option D: A sine wave with peak voltage +2V and a period of 0.5s, starting at 0 and initially decreasing.]
- 1
Analyse the effect of halving the rotation speed.
The magnitude of the induced voltage is proportional to the speed.
Halving the speed will halve the peak voltage from 2V to 1V.
The frequency of rotation is also halved, which means the time period for one cycle will double, from 1.0s to 2.0s.
This eliminates option D.
- 2
Analyse the effect of reversing the magnetic field direction.
The original graph starts at t=0 by increasing, meaning the induced voltage is initially positive.
Reversing the magnetic field will reverse the polarity of the induced voltage at every point in the cycle.
Therefore, the new graph must start at t=0 by decreasing, making the initial voltage negative.
- 3
Combine the effects.
We need a waveform with a peak voltage of 1V, a period of 2.0s, and it must be inverted compared to the original sine wave.
This means it should start at 0 and decrease towards its first trough.
- 4
Evaluate the options.
Option A has a peak voltage of 1V, a period of 2.0s, and starts by decreasing from zero.
Option B is incorrect because the coil starts horizontal (0 voltage), not vertical (peak voltage).
Option C has the correct amplitude and period but the wrong initial direction.
Answer: A
Common mistakes
- ×Sign errors are common when determining direction. Always use Lenz's Law: the induced effect *opposes* the change. If you push a north pole towards a coil, the coil must induce a north pole to repel it. This determines the current direction.
- ×Misinterpreting diagrams showing relative motion. If a magnet and a coil are moving together in the same direction at the same speed, there is no *relative* motion, so no voltage is induced. The key is that the conductor must be *cutting* field lines.
- ×Confusing the factors for AC generator output. Doubling the rotation speed doubles *both* the peak voltage (amplitude) and the frequency (halves the period). Students sometimes only change one of these on a graph.
- ×Forgetting that induction only occurs during a *change*. A stationary magnet inside a coil induces zero voltage, no matter how strong the magnet is.
No-calculator tips
- ✓Focus on proportionality. If a generator's speed is tripled, the peak voltage triples and the frequency triples. If the number of turns is doubled, the peak voltage doubles but the frequency is unchanged. Sketch the new graph relative to the old one.
- ✓Use logic for direction. You don't need complex equations. Ask: 'What must the induced field do to oppose the motion?' If a magnet is pulled away, the coil will induce a pole to attract it back.
- ✓When interpreting AC generator graphs, the peak voltage represents the moment the coil is moving fastest through the field lines (horizontal coil), and zero voltage occurs when it moves parallel to them (vertical coil).