Question

A coil having an area A₀ is placed in a magnetic field which
changes from B₀ to 4 B₀ in time interval t. The e.m.f. induced
in the coil will be
(a) 3A₀ B₀ / t (b) 4A₀ B₀ / t
(c) 3B₀ /A₀t (d) 4A₀ / B₀t

Answer 1

Given:

Coil has area $A_{0}$

Magnetic Field changes from $B_{0}$ to $4B_{0}$

Time taken = t

To find:

Emf induced in the coil

Concept:

We shall be applying Faraday's Electromagnetic Law of Induction , which states that the EMF induced in a coil shall be equal to the change in Magnetic Flux

Calculation:

Final magnetic flux be $\phi_{2}$.

$\phi_{2} = A_{0} \times 4B_{0}$

$=> \phi_{2} = 4A_{0}B_{0}$

Initial Magnetic Flux be $\phi_{1}$

$\phi_{1} = A_{0} \times B_{0}$

$=> \phi_{1} = A_{0}B_{0}$

So , change in Magnetic Flux :

$\therefore \: \:\Delta\phi$

$=(4-1)A_{0}B_{0}$

$=3A_{0}B_{0}$

Let EMF induced be E ;

$E = \dfrac{\Delta\phi}{t}$

$E = \dfrac{3A_{0}B_{0}}{t}$