Question 39: Magnetism and Matter

Question

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 :

Accepted Answer

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 	imes 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} 	imes V $
Here, $V$ is the volume of the solenoid, calculated as $A 	imes \ell$ (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} 	imes A \ell $
This formula gives us the magnetic energy stored in the solenoid.

Answer

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

Answer

$\frac{\mathrm{B}^2 \mathrm{~A} l}{2 \mu_0}$

Answer

$\frac{\mathrm{B}^2 \mathrm{~A} l}{\mu_0}$

Answer

$\mathrm{B}^2 \mathrm{Al}$

Magnetism and Matter

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 :

Choose the correct answer: