Magnetic energy density

Advanced

Energy stored per volume.

Key relationu = B²/2μ₀

u = B²/(2μ₀); for B = 1 T that's 400 kJ/m³, much more than the electric energy density at practical fields.

Worked example

MRI magnet stores megajoules.

Common mistake

Compare ½ε₀E².

In more detail

The energy density of a magnetic field is u = B²/(2μ0), the energy stored per unit volume. It is the magnetic analogue of electric energy density.

Estimating energy stored in magnetic fields of motors and coils.
Magnetic energy in plasma confinement is calculated this way.
Engineers designing magnetic systems estimate the energy stored in the field per unit volume.

What units does it have?

Joules per cubic metre.

Is magnetic energy stored in the field?

Yes, the field is the storage medium, just as for electric energy.

Why does the energy density depend on B squared?

The energy stored in a field grows with the square of its strength, as with the electric energy density.