What do you mean by magnetic energy?

Magnetic Energy

If a steady current flows through an inductor, a time-independent magnetic field is created. If suddenly the current source is disconnected, the change in the enclosed magnetic flux will generate a self-induced emf which will try to keep the current flowing in the original direction. The electric energy delivered by the self-induced emf was originally stored in the inductor in the form of magnetic energy. The amount of magnetic energy stored in the magnetic field can be determined by calculating the total power delivered by the power source to create the magnetic field. Suppose that after the battery is connected to the inductor the current increases at a rate of dI/dt. The self-induced emf created by this time-dependent current is equal to

The current must deliver extra power to overcome this self-induced emf. The power required will be time dependent and is equal to

The work done by the current is stored in the inductor as magnetic energy. The change dU in the magnetic energy of the inductor is thus equal to

The total energy stored in the magnetic field of the inductor when the current reaches its final value can be obtained by integrating eq. between I = 0 and I = I_f.

For a solenoid of length l the self-inductance is equal to

The magnetic energy stored in the solenoid is thus equal to

where V is the volume of the solenoid. The magnetic energy can be expressed in terms of B and V:

where B = u₀ n I is the magnetic field in the solenoid. The total magnetic energy of an inductor can now be expressed in terms of the magnetic energy density u which is defined as

The magnetic energy stored in the magnetic field is equal to the energy density time the volume. Although we have derived the formula for the magnetic energy density for the special case of a very long solenoid, its derivation is valid for any arbitrary magnetic field.