# Lenz's law

The direction of the induced e.m.f. was explained by Lenz who proposed the following law in 1835:

The direction of the induced e.m.f. is such that it tends to oppose the change that produced it.

We can explain this law by considering the energy changes that occur when a magnet is moved towards a coil, as shown in Figure 1. Assume that the mag- net is moved towards the coil with its north pole facing towards the coil. Now by Lenz's law this should induce a current in the coil such that the right-hand end of the coil (B) nearest the magnet is also a north pole. If this is true then it should repel the magnet and work must be done on the magnet to move it in against this repulsion.

The energy used goes to produce the induced e.m.f. in the coil.

This would agree with Lenz's law.

However, if we assume that the e.m.f produced is in the opposite sense and gives a south pole at B then as the magnet is moved in it will experience an attraction due to the e.m.f. in the coil. This will accelerate it, the e.m.f. produced will increase in size, the acceleration will increase and so on.

Clearly energy is being produced from nothing and this is impossible.

## Back e.m.f

Since the e.m.f generated opposes the changes that produce it, it is known as a back e.m.f. This effect is particularly important in electric motors.