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Solved Problems-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.
We have self-inductance of a long solenoid given as, Description: Description: 108695.png
Hence, the magnetic energy stored in the solenoid is,
Description: Description: 108685.png
Description: Description: 108675.png
The result can be expressed in terms of the magnetic field as,
Description: Description: 108667.png
Since Description: Description: 108657.png is the volume within the solenoid, and the magnetic field inside the solenoid is uniform, the term Description: Description: 108649.png may be considered as the magnetic energy density.

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