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Q.
The $rms$ value of the electric field of the light coming from the sun is $720 \,N \,C^{-1}$. The average total energy density of the electromagnetic wave is
Electromagnetic Waves
Solution:
Total average energy density of electromagnetic wave is
$U_{av} = \frac{1}{2} \varepsilon_{0} E^{2}_{rms} + \frac{1}{2\mu_{0}}B^{2}_{rms}$
$= \frac{1}{2} \varepsilon _{0} E^{2}_{rms} + \frac{1}{2\mu _{0}}\left(\frac{E^{2}_{rms}}{c^{2}}\right)$
$\left(\because B_{rms} = \frac{E_{rms}}{c}\right)$
$= \frac{1}{2} \varepsilon _{0} E^{2}_{rms} + \frac{1}{2\mu _{0}}E^{2}_{rms} \varepsilon_{0}\mu_{0}$
$\left(\because\quad c = \frac{1}{\sqrt{\mu _{0}\varepsilon _{0} }}\right)$
$= \frac{1}{2} \varepsilon _{0} E^{2}_{rms} + \frac{1}{2} E^{2}_{rms} = \varepsilon _{0} E^{2}_{rms}$
$= 8.85 \times 10^{-12} \times \left(720\right)^{2}$
$= 4.58 \times 10^{-6} \,J \,m^{-3}$