The average value of electric energy density | vedclass

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(D) The instantaneous electric energy density in an electromagnetic wave is given by $u_E = 1/2 \epsilon_0 E^2$.Since $E = E_0 \sin(\omega t - kx)$,we

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$1/4 \epsilon_0 E_0^2$

Vedclass · Answer

(D) The instantaneous electric energy density in an electromagnetic wave is given by $u_E = 1/2 \epsilon_0 E^2$.Since $E = E_0 \sin(\omega t - kx)$,we have $u_E = 1/2 \epsilon_0 E_0^2 \sin^2(\omega t - kx)$.The average value of $\sin^2(	heta)$ over a complete cycle is $1/2$.Therefore,the average electric energy density is $\langle u_E angle = 1/2 \epsilon_0 E_0^2 	imes \langle \sin^2(\omega t - kx) angle$.$\langle u_E angle = 1/2 \epsilon_0 E_0^2 	imes 1/2 = 1/4 \epsilon_0 E_0^2$.

The average value of electric energy density in an electromagnetic wave is. [where $E_0$ is peak value]

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