Question

A conducting loop of area $10{\text{cm}}^2$ is placed in a magnetic field which varies sinusoidally with time as $B=2\sin 100t$. The normal to the coil makes an angle of ${60}^{\circ }$ with direction of the field. Find the maximum magnetic flux through the coil.

• A. $2\text{mWb}$
• B. $0.2\text{mWb}$
• C. $1\text{mWb}$
• D. $0.1\text{mWb}$

Answer 1

The correct option is C $1\text{mWb}$

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

$B=2\sin 100t$

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

$\therefore$ Flux linked with the loop:

$\varphi =BA\cos \theta$

$\varphi =2\sin 100t\times 10\times {10}^{-4}\times \cos {60}^{\circ }$

$\varphi ={10}^{-3}\sin 100t$

For maximum flux, $\sin 100t=1$

$\Rightarrow {\varphi }_{max}={10}^{-3}\text{Wb}=1\text{mWb}$

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