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In a plane e.m. wave, the electric field varies with time having an amplitude 1Vm^-1. The frequency of wave is 0.5xx10^(15) Hz. The wave is propagating along Z-axis. What is the average energy density of (i) electric field (ii) magnetic field (iii) total (iv) what is the amplitude of magnetic field?

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Answer Text

Answer :
(i) `2.21xx10^(-12)Jm^-3, (ii) 2.21xx10^(-12)Jm^-3 (iii) 4.42xx10^(-12)Jm^-3 (iv) 3.3xx10^-9J`
Solution :
(i) Average energy density of electric field, <br> `u_E=1/2 in_0 E_(rms)^2=1/2in_0 ((E_0)/(sqrt2))^2 ( :' E_(rms)=(E_0)/(sqrt2))` <br> `=1/4in_0E_0^2=1/4xx(8.854xx10^(-12))xx1^2` <br> `=2.21xx10^(-12)Jm^-3` <br> (ii) Average energy density of magnetic field, <br> `u_B`=average energy density of electric field <br> `=2.21xx10^(-12)Jm^-3` <br> (iii) Total average energy density, <br> `u=u_E+u_B=2u_E=2xx2.21xx10^(-12)` <br> `=4.42xx10^(-12)Jm^-3` <br> (iv) Amplitude of magnetic field, <br> `B_0=E_0//c=1//(3xx10^8)=3.33xx10^-9T`

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