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 :

<p>To determine the magnetic energy stored in a solenoid filled with a material of relative permeability 2, we start with the expression for energy density in a magnetic field:</p> <p>$ \frac{U}{V} = \frac{B^2}{2 \mu_{\mathrm{r}} \mu_0} $</p> <p>Given that the relative permeability $\mu_{\mathrm{r}}$ is 2, this becomes:</p> <p>$ \frac{U}{V} = \frac{B^2}{2 \times 2 \mu_0} = \frac{B^2}{4 \mu_0} $</p> <p>The energy $U$ stored in the solenoid can be expressed as:</p> <p>$ U = \frac{B^2}{4 \mu_0} \times V $</p> <p>Here, $V$ is the volume of the solenoid, calculated as $A \times \ell$ (where $A$ is the cross-sectional area and $\ell$ is the length). Therefore, substituting for $V$, we get:</p> <p>$ U = \frac{B^2}{4 \mu_0} \times A \ell $</p> <p>This formula gives us the magnetic energy stored in the solenoid.</p>