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:

$ \frac{U}{V} = \frac{B^2}{2 \mu_{\mathrm{r}} \mu_0} $

Given that the relative permeability $\mu_{\mathrm{r}}$ is 2, this becomes:

$ \frac{U}{V} = \frac{B^2}{2 \times 2 \mu_0} = \frac{B^2}{4 \mu_0} $

The energy $U$ stored in the solenoid can be expressed as:

$ U = \frac{B^2}{4 \mu_0} \times V $

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:

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

This formula gives us the magnetic energy stored in the solenoid.