Question

A coil having an area $A_0$ is placed in a magnetic field. The field intensity changes from $B_0$ to $4B_0$ in time interval of ‘t’. The magnitude of emf induced in the coil will be _____.

• A. $\frac{A_0{B}_0}{t}$
• B. $\frac{3A_0{B}_0}{t}$
• C. $\frac{3B_0}{A_{0}t}$
• D. $\frac{4B_0}{A_{0}t}$

Answer 1

The correct option is B $\frac{3A_0{B}_0}{t}$

The emf induced in a coil of turns $N$, area of cross section $A$ is given by

$emf=-\frac{\Delta \left(BA\right)}{t}$ $=-A_0(4B_0-B_0)$

where $B_2-B_1$ is the change in the magnetic field.
$⟹e=\frac{-3A_0{B}_0}{t}$

Hence, the magnitude $|e|=\frac{3A_0{B}_0}{t}$