Question

A conducting loop of area $5.0{\text{cm}}^2$ is placed in a magnetic field which varies sinusoidally with time as $B=B_0\sin \omega t$ where $B_0=0.20\text{T}$ and $\omega =300s^{-1}$. The normal to the coil makes an angle of ${60}^{\circ }$ with direction of the field. Find the maximum emf induced in the coil.

• A. $1.5\text{V}$
• B. $0.15\text{V}$
• C. $0.015\text{V}$
• D. $3\text{V}$

Answer 1

The correct option is C $0.015\text{V}$

Area of the loop $\left(A\right)=5\times {10}^{-4}{\text{m}}^2$

$B=0.2\sin 300t$

$\theta ={60}^{\circ }$

$\therefore$ Flux linked with the loop:

$\varphi =BA\cos \theta$

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

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

Now, emf indcued in the loop is,

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

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

$\Rightarrow E=15\times {10}^{-3}\cos 300t$

For maximum emf $\cos 300t=1$

$\Rightarrow E_{max}=1.5\times {10}^{-2}\text{V}=0.015\text{V}$

Hence, option ($C$) is the correct answer.