A solenoid having area $A$ and length ' $l$ ' is filled with a material having relative permeability 2. The…

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 :
  1. $\frac{\mathrm{B}^2 \mathrm{~A} l}{\mu_0}$
  2. $\frac{\mathrm{B}^2 \mathrm{~A} l}{2 \mu_0}$
  3. $\mathrm{B}^2 \mathrm{Al}$
  4. $\frac{\mathrm{B}^2 \mathrm{~A} l}{4 \mu_0}$

Solution

$\frac{\mathrm{U}}{\mathrm{V}}=\frac{\mathrm{B}^2}{2 \mu_{\mathrm{r}} \mathrm{u}_0} \Rightarrow \mathrm{U}=\frac{\mathrm{B}^2}{4 \mu_0} \mathrm{~V}=\frac{\mathrm{B}^2}{4 \mu_0} \mathrm{~A} \ell$

Asked in: JEE Main 2025 (02 Apr Shift 2)

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