Q 12-06-100JEE MainJEE Main 2022 (27 Jul, Shift 2)Easy
A conducting circular loop is placed in $X$-$Y$ plane in presence of magnetic field $\vec B = (3t^3\hat j + 3t^2\hat k)$ in SI unit. If the radius of the loop is $1$ m, the induced emf in the loop, at time, $t = 2$ s is $n\pi$ V. The value of $n$ is ______ .
Numerical value type. Enter your answer.
Answer: 12
Only the $z$-component threads a loop in the $X$-$Y$ plane:
$$\Phi = B_z\pi r^2 = 3t^2\pi$$
$$|\varepsilon| = \frac{d\Phi}{dt} = 6\pi t = 12\pi\ \text{V at } t = 2\ \text{s}$$
$n = 12$.
Solution by Sreeraj P, M.Sc Physics