Obtain the expression for the magnetic energy stored in an ideal inductor of self inductance L when a current I passes through it.
Hence obtain the expression for the energy density of magentic field produced in the inductor.

Explanation

Work done aginst the induced emf in building up the current O to I in
`W=intdw=intEldt=intL(dl)/(dt).ldt`
`impliesunderset(0)overset(I)intLIdI=(1)/(2)LI^(2)`
This is magnetic energy stored in solenoid.
`U_(B)=W=(1)/(2)LI^(2)=(1)/(2)L((B)/(mu_(0)n))" "[:'B=mu_(0)nI]`
`U_(B)=(1)/(2)mu_(0)n^(2)Al((B)/(mu_(0)n))^(2)" "[:'L=mu_(0)n^(2)Al]`
So, magnetic energy density `U_(B)=(U_(B))/(Al)impliesU_(B)implies(B^(2))/(2mu_(0))`.