The expression for the magnetic energy stored | vedclass

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(A) The magnetic energy density $u_B$ in a magnetic field $B$ is given by the formula:$u_B = \frac{B^2}{2 \mu_0}$Since the energy density is defined a

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$\frac{1}{2 \mu_0} B^2 AL$

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(A) The magnetic energy density $u_B$ in a magnetic field $B$ is given by the formula:$u_B = \frac{B^2}{2 \mu_0}$Since the energy density is defined as energy per unit volume $(u_B = \frac{U}{V})$,the total energy $U$ stored in a volume $V$ is:$U = u_B 	imes V$The volume $V$ of a solenoid with length $L$ and cross-sectional area $A$ is $V = A 	imes L$.Substituting the values,we get:$U = \left( \frac{B^2}{2 \mu_0} ight) 	imes (A L) = \frac{1}{2 \mu_0} B^2 AL$

The expression for the magnetic energy stored in a solenoid of length $L$,in terms of magnetic field $B$ and area $A$ is

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