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?

Answer

(i) `2.21xx10^(-12)Jm^-3, (ii) 2.21xx10^(-12)Jm^-3 (iii) 4.42xx10^(-12)Jm^-3 (iv) 3.3xx10^-9J`

Explanation

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