# 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 :

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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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