Q 12-06-151JEE MainJEE Main 2025 (2 Apr, Shift 2)Medium
A solenoid having area $A$ and length $l$ is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is:
Answer: (D) $\dfrac{B^2Al}{4\mu_0}$
Inside a magnetic material the energy density is $u = \dfrac{B^2}{2\mu} = \dfrac{B^2}{2\mu_r\mu_0}$. With $\mu_r = 2$:
$$u = \frac{B^2}{4\mu_0}$$
The field is uniform inside the solenoid, of volume $Al$:
$$U = \frac{B^2Al}{4\mu_0}$$
Solution by Sreeraj P, M.Sc Physics