1. Magnetic energy density in a medium

The magnetic energy density is

$u = \frac{1}{2}BH$

For a linear magnetic medium,

$B = \mu H = \mu_0 \mu_r H$

So,

$H = \frac{B}{\mu} = \frac{B}{\mu_0 \mu_r}$

Hence,

$u = \frac{1}{2}B\left(\frac{B}{\mu_0 \mu_r}\right)=\frac{B^2}{2\mu_0\mu_r}$

2. Given relative permeability

Here,

$\mu_r = 2$

Therefore,

$u = \frac{B^2}{2\mu_0 \cdot 2} = \frac{B^2}{4\mu_0}$

3. Total energy stored in the solenoid

Volume of the solenoid is

$V = A l$

So total magnetic energy stored is

$U = uV = \frac{B^2}{4\mu_0} \cdot Al$

Thus,

$U = \frac{B^2 A l}{4\mu_0}$

4. Matching with options

This corresponds to:

Option A:

$\frac{B^2 A l}{4\mu_0}$