A conducting circular loop is placed in X - Y plane in presence of magnetic field B = (3t³j + 3t²k) in SI unit. If the radius of the loop is 1 m, the induced emf in the loop, at time, t = 2 s is nπ V. The value of n is ___________. Numerical answer type. Work it out, then open the answer.

Answer: 12. Loop in the XY plane: area vector along k, so only Bz = 3t² gives flux. φ = 3t² × π(1)² = 3π t² e = (dφ)/(dt) = 6π t = 12π V at t = 2 s So n = 12.

A conducting circular loop is placed in X - Y plane in presence of… | JEE Main 2022 (27 Jul, Shift 2)

Q57JEE Main 2022 · 27 JUL · SHIFT 2Medium

Magnetic Flux & Faraday's Law

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

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 12

Loop in the XY plane: area vector along $\hat{k}$ , so only $B_z = 3t^2$ gives flux.
$\phi = 3t^2 \times \pi(1)^2 = 3\pi t^2$
$e = \frac{d\phi}{dt} = 6\pi t = 12\pi$ V at $t = 2$ s
So $n = 12$ .

Report a mistake

Magnetic Flux & Faraday's Law question from JEE Main 2022 (27 Jul, Shift 2)

More questions on Magnetic Flux & Faraday's Law