Question

A region in free space has a magnetic field Intensity of Bwb/m2. What is the energy stored per m3 of space​

Answer 1

Given:

A region in free space has a magnetic field Intensity of B Wb/m2.

To Find:

What is the energy stored per m3 of space​?

Solution:

Since, we know that-

• Magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetized materials.
• Electric field is a scaler field  that surrounds each electric charge and exerts force.

The formula for the energy stored in a magnetic field is

$\[U = \frac{1}{2}L{I^2}\]$

Now putting expression of L and I in equation of U, we get new expression i.e.

$\[U = \dfrac{{{B^2}Al}}{{2{\mu _0}}}\]$

Where, B is the magnetic field intensity,  A is the effective cross-sectional area of the coil and l is the effective length of the coil.

therefore, energy stored per m^3 of space having B Wb/m^2 magnetic field intensity is-

$\[\begin{gathered} U/{m^3} = \frac{{{B^2}Al}}{{2{\mu _0}}}/{m^3} \hfill \\ = \frac{{{B^2}}}{{2{\mu _0}}} \hfill \\ \end{gathered} \]$        (Since, here, Al=Vol.(V)=m^3)