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
Concept. Area fixed, field changing: $\varepsilon=A\dfrac{dB}{dt}$.
Step 1. Rate. $\dfrac{dB}{dt}=4t+2=14$ T/s at $t=3$.
Step 2. Emf. $\dfrac{22}{7}\times0.04\times14=1.76$ V.
Step 3. Current. $\dfrac{1.76}{2}=0.88=\dfrac{44}{50}$ A.
Answer. $\alpha=44$.
Solution by Sreeraj P, M.Sc Physics
