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Electromagnetic Induction and Faraday's Law
Electromagnetism
Moving a magnet near a coil of wire can produce electricity without any battery. This is electromagnetic induction, the principle behind every large-scale generator.
What induction is
Electromagnetic induction is the production of an electromotive force, or e.m.f., in a conductor when the magnetic flux through it changes. Flux can change because the field strength changes, the area of the loop changes, or the loop turns relative to the field. Any of these changes induces a voltage across the ends of the conductor, and if the circuit is closed a current flows. The effect was discovered by Michael Faraday in 1831, and it is remarkable because no battery or direct electrical connection is needed: motion and magnetism alone create the voltage. The induced e.m.f. lasts only while the flux is changing.
Faraday's and Lenz's laws
Faraday's law gives the size of the induced e.m.f.: it equals the rate of change of magnetic flux, multiplied by the number of turns in the coil. A faster change, a stronger field, a larger area or more turns all increase the e.m.f. Lenz's law gives the direction: the induced current flows in the direction that opposes the change producing it, which is a consequence of the conservation of energy. If the induced current helped the change along, it would create energy from nothing. Together the two laws explain generators, transformers and induction hobs, and the minus sign in the formula is Lenz's law in mathematical form.
Where you see it
In a power station, a turbine spins a coil in a magnetic field, or magnets past a coil, producing alternating current for the grid. A bicycle dynamo and a hand-crank torch use the same idea on a small scale. Transformers use induction to step voltage up for long-distance transmission and down again for safe use in homes, with almost no energy loss. Induction hobs heat a pan directly by inducing currents in its base, and metal detectors and contactless chargers also rely on changing magnetic fields. Even the regenerative braking in an electric car uses induction to recover energy.
Worked example: e.m.f. induced in a coil
A coil of 100 turns sits in a magnetic field. The flux through one turn changes by 0.020 Wb in 0.050 s. Use induced e.m.f. = N x (change in flux) / (time taken). Substitute: e.m.f. = 100 x 0.020 / 0.050. 100 x 0.020 = 2.0. 2.0 / 0.050 = 40 V. The induced e.m.f. is 40 V. By Lenz's law its direction opposes the change in flux that caused it.
Common mistakes
- Forgetting the number of turns N: the total e.m.f. is N times the rate of change of flux through one turn.
- Confusing flux with field: flux depends on field strength, area and angle, so turning a coil can change flux even if B is constant.
- Ignoring Lenz's law: the induced current always acts to oppose the change that produced it, which fixes its direction.
Practice questions
- A 50-turn coil sees its flux change by 0.010 Wb in 0.20 s. What e.m.f. is induced?
Show answer
e.m.f. = 50 x 0.010 / 0.20 = 2.5 V.
- If the area of a loop is doubled, how does the induced e.m.f. change for the same rate of change of B?
Show answer
The flux increases by 2^2 = 4, so the e.m.f. becomes 4 times larger.
- A magnet is pushed into a coil. What does Lenz's law say about the induced current?
Show answer
The induced current flows so its own magnetic field opposes the increase, i.e. it tries to push the magnet back out.
Frequently asked questions
Why do transformers only work with a.c.?
Induction needs a changing flux, so a steady d.c. current in the primary produces no e.m.f. in the secondary; only changing or alternating current works.
Can a magnet alone generate electricity?
Yes, by moving a magnet through a coil or spinning a coil in a field, exactly as a generator does.