Q. The energy associated with electric field is $(U_E)$ and with magnetic field is $(U_B)$ for an electromagnetic wave in free space. Then :

Solution:

Average energy density of magnetic field,
$u_{B} = \frac{B_{0}^{2}}{2 \mu_{0}} , B_{0} $ is maximum value of magnetic field.
Average energy density of electric field,
$u_{E} = \frac{\varepsilon_{0} \in^{2}_{0}}{2}$
now, $ \in_{0} =CB_{0} , C^{2} = \frac{1}{\mu_{0} \in_{0} } $
$ u_{E} = \frac{\in_{0}}{2} \times C^{2} B^{2}_{0} $
$ = \frac{\in_{0}}{2} \times\frac{1}{\mu_{0} \in_{0}} \times B^{2}_{0} = \frac{B^{2}_{0}}{2 \mu_{0}} = u_{B}$
$ u_{E} = u_{B} $
since energy density of electric & magnetic field is same, energy associated with equal volume will be equal.
$ u_{E} = u_{B} $

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