Question

At time $t=0$ magnetic field of $1000\text{G}$ is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to $500\text{G}$, in the next $5\text{s}$, then induced $EMF$ in the loop is:

• A. $56\mu \text{V}$
• B. $28\mu \text{V}$
• C. $48\mu \text{V}$
• D. $36\mu \text{V}$

Answer 1

The correct option is A $56\mu \text{V}$

Using Faraday's law of induction,

$E=-\frac{d\varphi }{dt}=-A\frac{dB}{dt}$

According to question,

$dB=500-1000=-500\text{G}$
$\Rightarrow dB=-500\times {10}^{-4}\text{T}$
$\text{Time},dt=5\text{s}$

$\Rightarrow \frac{dB}{dt}=\frac{-500\times {10}^{-4}\text{T}}{5\text{s}}=-{10}^{-2}{\text{Ts}}^{-1}$


Area of closed loop,

$\text{A = (area of}\square )\text{-(2 area of}△)$

$A=(16\times 4)-(2\times \frac{1}{2}\times 2\times 4){\text{cm}}^2$
$\Rightarrow A=56\times {10}^{-4}{\text{m}}^2$
$\therefore E=-A\frac{dB}{dt}=56\times {10}^{-4}\times {10}^{-2}$

$\Rightarrow E=56\times {10}^{-6}\text{V}=56\mu \text{V}$

Hence, option $\left(A\right)$ is correct.