Question

A 65-turn coil has a diameter of 14 cm. Find the magnitude of the emf induced in the coil (in V) if it is placed in a spatially uniform magnetic field of magnitude 0.65 T so that the face of the coil makes the following angles with the magnetic field, and the magnetic field is reduced to zero uniformly in 0.2 s.

Answer 1

Answer:

The value is $\epsilon = 3.24 \ V$  

Explanation:

From the question we are told  that

    The number of turns is  n =  65

    The diameter is  $d = 14 \ cm = 0.14 \ m$

    The magnetic field is  $B_1 = 0.65 \ T$

    The time taken for the magnetic field to be reduced to $B_2 = 0 \ T$ is $\Delta t = 0.2 s$

Generally the magnitude of the induced emf is mathematically represented as

        $\epsilon = N * \frac{B_1 - B_2}{\Delta t } * A$

Here A is the area of the coil which is mathematically represented as

        $A = \pi * \frac{d^2}{4}$

=>     $A = 3.142 * \frac{0.14^2}{4}$

=>     $A = 0.0154 \ m^2$

So

        $\epsilon = 65 * \frac{0.65 - 0 }{0.2 } * 0.01534$  

=>    $\epsilon = 3.24 \ V$