# Solved Problems-16

Problem-16
A long solenoid with length l and a radius R consists of N turns of wire. A current I passes through the coil. Find the energy stored in the system.
Solution
We have self-inductance of a long solenoid given as,
Hence, the magnetic energy stored in the solenoid is,

The result can be expressed in terms of the magnetic field as,

Since  is the volume within the solenoid, and the magnetic field inside the solenoid is uniform, the term  may be considered as the magnetic energy density.