We have seen that we can induce an EMF by changing the amount of magnetic field in a circuit. We can do this by moving a wire through a magnetic field or moving a magnet near to a coil. But what do we mean by amount of magnetic field?

4.11 We can change the flux in a circuit by moving a wire or changing the field strength.

Magnetic flux

Picture 4.11 shows a wire moving through a magnetic field. We represent the magnetic field with magnetic field lines (in this case, they are going into the screen and are shown as crosses). As the wire moves through the field, the number of field lines enclosed by the circuit increases. So the total field in the circuit has gone up. We call this the magnetic flux. It has the symbol f - (phi to rhyme with fly).

There is another way of increasing the flux in the circuit: make the field stronger. This is like bringing a magnet closer to the circuit.

You can think of the flux as being represented by the number of field lines. We sometimes call them lines of magnetic flux. The closer together the lines of flux, the stronger the field. That is, the strength of the field is represented by the density of the lines of flux. We sometimes call the magnetic field strength, B, the magnetic flux density. And we use this idea to define flux:

Faraday's Law

We have seen that the faster we move a wire, the bigger the EMF we induce. In fact, we find that the EMF is proportional to the rate at which the flux changes. So, in a simple circuit:

This means that if we double the speed of the wire, the flux in the circuit increases at twice the rate. Therefore, the EMF is twice as big.

We can increase the total flux linking a circuit by using a coil rather than a single piece of wire. In which case, the EMF, E, will increase in proportion with the number of coils, N. So we get an expression for Faraday's Law:

Notice the minus sign in the equation. This is to indicate that the induced EMF opposes the change in flux that produced it.