Electromagnetic Induction

Electromagnetic induction is the process of producing a voltage when the magnetic environment of a conductor changes. It is the basic principle behind electric generators, transformers, and many everyday technologies. In a generator, mechanical energy is converted into electrical energy by moving a coil through a magnetic field. Understanding this idea helps explain how power plants and small hand-crank devices make electricity.

A rotating coil between the north and south poles of a magnet experiences a changing magnetic flux. As the angle of the coil changes, the amount of magnetic field passing through it changes, and this induces an emf according to Faraday's law. The direction of the induced current is determined by Lenz's law, which says the induced current opposes the change that caused it. Faster rotation, stronger magnets, and more turns in the coil all increase the induced voltage.

Key Facts

Faraday's law: emf = -N(dPhi/dt)
Magnetic flux: Phi = BA cos(theta)
For a rotating coil, flux changes because theta changes with time.
Greater N, greater B, greater A, or faster rotation gives larger induced emf.
Lenz's law: the induced current creates a magnetic effect that opposes the change in flux.
In a simple generator, mechanical work on the coil is converted into electrical energy.

Vocabulary

Electromagnetic induction: The production of a voltage in a conductor because the magnetic flux through it changes.
Magnetic flux: A measure of how much magnetic field passes through a surface, given by Phi = BA cos(theta).
EMF: Electromotive force is the induced voltage that drives charge around a circuit.
Faraday's law: The law stating that induced emf equals the negative rate of change of magnetic flux times the number of turns.
Lenz's law: The rule that the induced current flows in a direction that opposes the change in magnetic flux.

Common Mistakes to Avoid

Using Phi = BA for every situation, which is wrong because the angle matters and the correct expression is Phi = BA cos(theta).
Forgetting the negative sign in Faraday's law, which is wrong because the sign shows the direction effect described by Lenz's law.
Assuming a magnetic field alone always induces current, which is wrong because current is induced only when the flux changes.
Thinking the current is largest when the flux is largest, which is wrong because emf depends on how fast flux changes, not on the flux value itself.

Practice Questions

1 A coil has 50 turns and an area of 0.020 m^2. It is perpendicular to a uniform magnetic field of 0.40 T. What is the magnetic flux through one turn?
2 A 200-turn coil experiences a change in magnetic flux from 0.030 Wb to 0.010 Wb in 0.50 s. What is the magnitude of the average induced emf?
3 A coil rotates steadily in a magnetic field. Explain why the induced current changes direction every half turn.