Faraday’s Law
Contents
21. Faraday’s Law#
Our discussion of both the Biot-Savart and Ampère’s laws tells us that moving charges (currents) produce magnetic fields. Since these currents are pushed by potential difference - driven by electric fields, these result in a magnetic field. The next question is can we start with a magnetic field and finish with an electric field - Faraday’s law tells us yes!
Thinking again about the link between moving charges and magnetic fields:
As we mentioned previously, we can think of
and we call this the electromotive force (EMF), denoted by
One potential question here is, as we saw in Fig. 18.8, an element of current carrying wire
If we have a coil of wire, with
Note that the two sides of Equation (21.1) differ by a sign, this is known as Lenz’s law. This is here to ensure that we do not
violate conservation of energy - the direction of an induced current which is pushed by the EMF

Fig. 21.1 Direction of induced EMF from a moving magnetic into a coil, Left - North pole moving into coil, Right - North pole moving out of coil.#
21.1. Electrical Transformers#
We can apply Faraday’s law to investigate the flow of magnetic fields and EMF’s in a transformer, as depicted in Fig. 21.2, where an initial
voltage

Fig. 21.2 Flow of magnetic flux in a transformer - we denote the left hand coil the Primary and right hand coil the Secondary, each carries a current
The alternating voltage in the primary circuit, say:
with some ohmic resistance
through the primary coil. The total input energy in the primary coil therefore is:
and this is related to the output energy
Since the magnetic flux moves through the iron core (and ignoring any losses), then we can combine the equations to find:
where