Question

A conducting circular loop is placed in X -Y plane in presence of magnetic field
$\stackrel{→}{B} = (3t^3\hat{j}+3t^2\hat{k})$ in SI unit. If the radius of the loop is 1 m, the induced emf in the loop at time $t = 2s$ is $nπV$. The value of $n$ is ______.

Answer 1

The correct answer is 12
$B_⊥=3t^2$
$\frac{dB_⊥}{dt} = 6t = 12 at\ t = 2$
$\frac{d\phi_1}{dt} = 12×π(1)^2$
$= 12π$
Therefore , value of $n$ is 12.