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(D) The intensity $I$ of a plane electromagnetic wave is related to the amplitude of the electric field $E_0$ by the formula: $I = \frac{1}{2} \epsilo

Vedclass · Accepted Answer

$200$

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(D) The intensity $I$ of a plane electromagnetic wave is related to the amplitude of the electric field $E_0$ by the formula: $I = \frac{1}{2} \epsilon_0 E_0^2 c$. Rearranging the formula to solve for $E_0$,we get: $E_0 = \sqrt{\frac{2 I}{\epsilon_0 c}}$. Given values are: $I = 53.1 \ W \ m^{-2}$,$\epsilon_0 = 8.85 	imes 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$,and $c = 3 	imes 10^8 \ m \ s^{-1}$. Substituting these values into the equation: $E_0 = \sqrt{\frac{2 	imes 53.1}{8.85 	imes 10^{-12} 	imes 3 	imes 10^8}}$. $E_0 = \sqrt{\frac{106.2}{26.55 	imes 10^{-4}}} = \sqrt{4 	imes 10^4} = 200 \ N \ C^{-1}$.

The amplitude of the electric field in a parallel beam of plane electromagnetic waves of intensity $53.1 \ W \ m^{-2}$ is (Permittivity of free space $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$) (in $N \ C^{-1}$)

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