Apply Faraday's and Lenz's laws to electromagnetic induction, generators and transformers.

What this dot point is asking

Electromagnetic induction is the reverse of the motor effect: instead of using a current to make motion, you use motion or a changing field to make a current. It is the basis of almost all electrical power generation.

Magnetic flux

Magnetic flux $\Phi$ measures how much magnetic field passes through a loop of area $A$:

where $\theta$ is the angle between the field and the normal (perpendicular) to the loop. Flux is measured in webers. Flux changes if the field strength changes, the area changes, or the loop rotates relative to the field.

Faraday's law

Faraday found that an EMF (voltage) is induced whenever the flux through a circuit changes. The size of the induced EMF is:

where $N$ is the number of turns in the coil and $\dfrac{\Delta\Phi}{\Delta t}$ is the rate of change of flux. The faster the flux changes and the more turns the coil has, the larger the induced EMF. A steady, unchanging flux induces nothing; only change matters.

Motional EMF

A special case is a straight conductor of length $L$ moving at speed $v$ perpendicular to a field $B$. The free charges in the conductor feel the magnetic force $qvB$ and pile up at the ends until an electric field balances it, giving a motional EMF:

This is the same physics as Faraday's law: as the rod moves it sweeps out area, so the flux through the circuit it is part of changes at the rate $BLv$. It explains the voltage induced across an aircraft wing moving through Earth's field and the output of a simple generator.

Lenz's law

The negative sign in Faraday's law represents Lenz's law: the induced current flows in the direction that opposes the change in flux producing it. If the flux is increasing, the induced current creates a field to oppose the increase; if it is decreasing, the induced current tries to maintain it. Lenz's law is a statement of conservation of energy. If the induced current aided the change, you would get energy for free.

Generators and transformers

A generator is essentially a motor run in reverse. A coil is rotated in a magnetic field, so the flux through it changes continuously, inducing an alternating EMF. With slip rings the output is alternating current; with a split-ring commutator it can be made into pulsed DC.

A transformer changes the voltage of an AC supply. An alternating current in the primary coil produces a changing flux in an iron core, which induces an EMF in the secondary coil. For an ideal transformer:

A step-up transformer ($N_s > N_p$) raises voltage; a step-down transformer lowers it. Energy is conserved, so for an ideal transformer $V_p I_p = V_s I_s$. Transformers only work with AC because they need a continuously changing flux.

When tackling induction questions, identify what is causing the flux to change, apply Faraday's law for the size of the EMF, and use Lenz's law to argue the direction. For transformers, remember the turns ratio sets the voltage ratio and that real transformers lose some energy to heat in the core and windings.