Question

A square loop of side $b$ is rotated in a constant magnetic field $B$ at angular frequency $\omega$ as shown in figure. What is the emf induced in it?

• A. $b^{2}B\omega \sin \omega t$
• B. $bB\omega {\sin }^2\omega t$
• C. $b{B}^2\omega \cos \omega t$
• D. $b^{2}B\omega$

Answer 1

Answer: (A)

$b^{2}B\omega \sin \omega t$

At time $t$, angle rotated by loop is $\theta =\omega t$. This is also the angle between $\overrightarrow{B}$ and $\overrightarrow{S}$. Then
$\varphi =BS\cos \theta =B{b}^2\cos \omega t$
$e=\left|\frac{d\varphi }{dt}\right|=b^{2}B\omega \sin \omega t$