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Prove the energy stored in a current ind...

Prove the energy stored in a current inductor, per unit volume is `(B^(2))/(2mu_(0))`, where B is the magnetic field inside the inductor.

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When a current I flows through a solenoid of self inductance L, the energy stored in the space inside solenoid, is given by `U= (1)/(2)Li^(2)`
Now, self inductance `L = mu_(0)n^(2) xx A xx l`
where n is number of turns per unit length, A area of cross section and i is the length of solenoid. ` U= (1)/(2)(mu_(0)n^(2)A xx l)^(2)`
suppose the solenoid to be long enough, the magnetic field inside the solenoid is given by `B= mu_(0)nl`
thus `U= (1)/(2)(mu^(2)n^(2)l^(2) xx (1)/(mu_(0)) xx A xx L= (B^(2))/(2mu_(0)) xx Axx l)`
where `A xx I=v`(volume of space inside solenoid)
thus, `(U)/("VolumeV")= B^(2)/(2mu)`
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