Question

Explain the relation between the induced electromotive force and the sectional area of the secondary coil, while the number of turns of the secondary coil keeps constant.

Answer 1

The magnetic flux is a measure of the number of magnetic field lines passing through an area. If a loop of wire with an area A is in a magnetic field B, the magnetic flux is given by:

If the flux changes, an emf will be induced. There are therefore three ways an emf can be induced in a loop:

1. Change the magnetic field
2. Change the area of the loop
3. Change the angle between the field and the loop

Faraday's law of induction

We'll move from the qualitative investigation of induced emf to the quantitative picture. As we have learned, an emf can be induced in a coil if the magnetic flux through the coil is changed. It also makes a difference how fast the change is; a quick change induces more emf than a gradual change. This is summarized in Faraday's law of induction. The induced emf in a coil of N loops produced by a change in flux in a certain time interval is given by:

Recalling that the flux through a loop of area A is given by

Faraday's law can be written:

Hence, emf induced will be directly proportional to the sectional area of the secondary coil.