Question

A coil of wire containing N turns is in an external magnetic field that is at a LaTeX: 45^o45 o angle from the plane of the coil and is steadily changing. Under these circumstances, an emf V is induced in the coil. If both the rate of change of the magnetic field and the number of turns in the coil are now doubled (but nothing else changes), what will be the induced emf in the coil?

Answer 1

Here we have given that we have a coil of having N number of turns and is placed in external magnetic field that is changing. Now from the faraday laws of electro magnetic induction we have the concept that whenever a coil is placed in varying magnetic field then this coil will try to oppose this change in its own loop by inducing a emf in it and that emf is given as

E = - Nd(time varying flux)/dt ........1

Here N is the number of turns

Now we also know that,

Flux = B• A = BAcos(theta)

Where B is the time varying magnetic field , A is the area of the coil and theta the angle made between field and loop

So as the question says as we if If both the rate of change of the magnetic field and the number of turns in the coil are now doubled so that from the expression of emf we can say that emf directly dependent on both the B and N so that as we double the number of turns and magnetic field our emf would become fourfold form the previous value has to now oppose more flux passing through it so it will induce its emf in such a way that it can counter the effects of increased field so that emf becomes four times of its previous value.

That is,

New Emf (V') = - 2Nd(2BA)/dt = 4 (E).