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(D) The intensity $I$ of an electromagnetic wave at a distance $r$ from a point source is given by $I = \frac{P}{4 \pi r^2}$,where $P$ is the power of

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$2.7$

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(D) The intensity $I$ of an electromagnetic wave at a distance $r$ from a point source is given by $I = \frac{P}{4 \pi r^2}$,where $P$ is the power of the source.Also,the intensity is related to the rms electric field $E_{rms}$ by $I = \epsilon_0 c E_{rms}^2$.Equating the two expressions: $\frac{P}{4 \pi r^2} = \epsilon_0 c E_{rms}^2$.Rearranging for $P$: $P = 4 \pi r^2 \epsilon_0 c E_{rms}^2$.Given: $r = 3 \ m$,$E_{rms} = 3 \ N C^{-1}$,$\epsilon_0 = 8.854 	imes 10^{-12} \ C^2 N^{-1} m^{-2}$,and $c = 3 	imes 10^8 \ m s^{-1}$.Substituting the values: $P = 4 	imes 3.14 	imes (3)^2 	imes (8.854 	imes 10^{-12}) 	imes (3 	imes 10^8) 	imes (3)^2$.$P = 4 	imes 3.14 	imes 9 	imes 8.854 	imes 10^{-12} 	imes 3 	imes 10^8 	imes 9$.$P \approx 113.04 	imes 8.854 	imes 10^{-4} 	imes 27 \approx 270.2 	imes 10^{-2} \approx 2.7 \ W$.Thus,the power of the source is $2.7 \ W$.

If the rms value of the electric field of electromagnetic waves at a distance of $3 \ m$ from a point source is $3 \ N C^{-1}$,then the power of the source is (in $W$)

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