Q 12-06-030JEE MainJEE Main 2026 (8 Apr, Shift 2)Medium
A $30$ cm long solenoid has $10$ turns per cm and area of $5\ \text{cm}^2$. The current through the solenoid coil varies from $2$ A to $4$ A in $3.14$ s. The e.m.f. induced in the coil is $\alpha \times 10^{-5}$ V. The value $\alpha$ is ______.
Answer: (B) $12$
Concept. Solenoid $L=\mu_0n^2Al$; $\varepsilon=L\dfrac{dI}{dt}$.
Step 1. Inductance. $4\pi\times10^{-7}\times10^6\times5\times10^{-4}\times0.3=1.885\times10^{-4}$ H.
Step 2. Emf. $1.885\times10^{-4}\times\dfrac{2}{3.14}=1.2\times10^{-4}$ V.
Answer. $12\times10^{-5}$ V (Option B).
Solution by Sreeraj P, M.Sc Physics
