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 \(\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2\) )

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Correct Answer

(C) \(8.85\)

Detailed explanation

\(\overrightarrow{ E }=20 \sin \omega\left( t -\frac{ x }{ C }\right) \hat{ j } / C\)

Average energy density of an em wave \(=\frac{1}{2} \epsilon_0 E_0^2\)

\(\text { Energy stored }=\left(\frac{1}{2} \epsilon_0 E _0^2\right)(\text { volume })\)

\(=\frac{1}{2} \times 8.85 \times 10^{-12} \times(20)^2 \times\left(5 \times 10^{-4}\right) \,J\)

\(=8.85 \times 10^{-13}\,J\)

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