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The electric field in an electromagnetic wave is given as $\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} NC ^{-1}$ Where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5 \times 10^{-4}\, m ^3$ will be $.....\times 10^{-13}\,J$
(Given $\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2$ )
$28.5$
$17.7$
$8.85$
$88.5$
Solution
$\overrightarrow{ E }=20 \sin \omega\left( t -\frac{ x }{ C }\right) \hat{ j } / C$
Average energy density of an em wave $=\frac{1}{2} \epsilon_0 E_0^2$
$\text { Energy stored }=\left(\frac{1}{2} \epsilon_0 E _0^2\right)(\text { volume })$
$=\frac{1}{2} \times 8.85 \times 10^{-12} \times(20)^2 \times\left(5 \times 10^{-4}\right) \,J$
$=8.85 \times 10^{-13}\,J$
