Question

What is an example of magnetic energy?

Answer 1

Step 1: Assuming the quantities:

Magnetism is a concept introduced in physics to help you understand one of the fundamental interactions in nature, the interaction between moving charges.

When current is passed through long solenoid energy is stored in the inductor in the form of magnetic energy.
Consider along solenoid of radius $r$ and length $l$ having $n$ turns per unit length carrying current $i$

Step 2: Formula used
The magnetic field inside the solenoid is $B={\mu }_{0}ni$.
The inductance of the solenoid is $L={\mu }_0{n}^2\mathrm{\pi }{\mathrm{r}}^{2}l$

Step 3: Calculation for the energy stored in the solenoid

The energy stored in the solenoid
$$\begin{gathered} U=\frac{1}{2}L{i}^2 \\ U=\frac{1}{2}\left({\mu }_0{n}^2{\mathrm{\pi r}}^2\mathrm{l}\right)i^2 \\ U=\frac{1}{2{\mu }_0}\left({\mu }_{0}n{i}^2\right)V \end{gathered}$$

Where $V=\mathrm{\pi }{\mathrm{r}}^2\mathrm{l}$ is the volume of the solenoid,

So we get, the magnetic energy stored in the solenoid is $U=\frac{B^2}{2{\mu }_0}V$.
This is an example of magnetic energy.

Some examples of magnetic energy are electric motors, generators, loudspeakers, etc.