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  • In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 1010 Hz and amplitude 48 V m–1.Show that the average energy density of the E field equals the average energy density of the B field.

10.(c) In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 \times 10 ^{10} Hz  and amplitude 48 V m^{-1}.

Show that the average energy density of the E field equals the average energy density of the B field. [c = 3 \times 10^8 m s^{-1}. ]

Answers (1)

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The average energy density of the Electric field(UE) 

= \frac{1}{2}\epsilon E^{2}

=\frac{1}{2}\epsilon (Bc)^{2}                 (as E=Bc)

=\frac{1}{2}\epsilon \frac{B^{2}}{\mu \epsilon }                      (c=\frac{1}{\sqrt{\mu \epsilon }})  

=UB 

Therefore the average energy density of the electric field is equal to the average energy density of the Magnetic field.

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Sayak

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