Q 12-06-036JEE MainJEE Main 2026 (5 Apr, Shift 2)Medium
A circular loop of radius $20$ cm and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec{B} = (2t^2 + 2t + 3)$ T. At $t = 0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3$ s is $\dfrac{\alpha}{50}$ A. The value of $\alpha$ is ______. (Take $\pi = 22/7$)
Numerical value type. Enter your answer.
Answer: 44
$\dfrac{dB}{dt} = 4t + 2 = 14$ T/s at $t = 3$ s.
Area $= \dfrac{22}{7} \times 0.04 = \dfrac{0.88}{7}$ m². emf $= 14 \times \dfrac{0.88}{7} = 1.76$ V.
$I = \dfrac{1.76}{2} = 0.88$ A $= \dfrac{44}{50}$ A, so $\alpha = 44$.
Solution by Sreeraj P, M.Sc Physics