Question

The magnitude of induced emf on the closed surface of ring will be

• A. $\pi a^2{B}_0$
• B. $2a^2{B}_0$
• C. $zero$
• D. $\frac{1}{2}\pi a^2{B}_0$

Answer 1

The correct option is A $\pi a^2{B}_0$

Farady's law states that time varying magnetic flux can induce an e.m.f.
E = Electric field, Induced

$E=-\frac{d\varphi }{dt}$
where,

$magneticFLux=\varphi =\overrightarrow{B}.d\overrightarrow{A}$

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

$\varphi =\overrightarrow{B}.\overrightarrow{A}=\pi a^{2}B\left(t\right)=\pi a^2{B}_{o}t$

$|E|=\frac{d\varphi }{dt}=\frac{\pi a^2{B}_{o}t}{dt}=\pi a^2{B}_o$