Question

A conducting loop of area $5{\text{cm}}^2$ is placed in a magnetic field which varies sinusoidally with time as $B=0.2\sin 300t$. The normal to the coil makes an angle of ${60}^{\circ }$ with the field. The emf induced at $t=\frac{\pi }{900}\text{s}$, is

• A. $7.5\times {10}^{-3}\text{V}$
• B. $\text{Zero}$
• C. $15\times {10}^{-3}\text{V}$
• D. $20\times {10}^{-3}\text{V}$

Answer 1

The correct option is A $7.5\times {10}^{-3}\text{V}$

Given:

$B=0.2\sin 300t;A=5\times {10}^{-4}{\text{m}}^2$

$\theta ={60}^{\circ };t=\frac{\pi }{900}$

Magnetic flux is given by,

$\varphi =BA\cos \theta$

$=0.2\times \sin 300t\times 5\times {10}^{-4}\times \cos {60}^{\circ }$

$\Rightarrow \varphi =5\times {10}^{-5}\sin 300t$

Induced emf is given by,

$E_{ind}=|-\frac{d\varphi }{dt}|=\left|\frac{d}{dt}\right(5\times {10}^{-5}\sin 300t\left)\right|$

$=1500\times {10}^{-5}\cos 300t$

$E_{ind}(\text{at}t=\frac{\pi }{900})=1500\times {10}^{-5}\times \cos 300\times \frac{\pi }{900}$

$\Rightarrow E_{ind}=750\times {10}^{-5}=7.5\times {10}^{-3}\text{V}$

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