In an electromagnetic wave, the amplitude of electric field is `10V//m`. The frequency of wave is
`5xx10^14Hz`. The wave is propagating along Z-axis, find (i) the average
energy density of electric field (ii) the average energy density of
magnetic field (iii) the total average energy density of EM wave.

Explanation

Here, `E_0=10Vm^-1, v=5xx10^14Hz`.
(i) Average energy density due to electric field is
`u_E=1/2in_0E_(rms)^2=1/2in_0((E_0)/(sqrt2))^2 =1/4in_0E_0^2`
`=1/4xx(8.85xx10^-12)xx(10)^2=2.21xx10^-10J//m^3`
(ii) Average energy density due to magnetic field is
`u_B=1/2 (B_(rms)^2)/(mu_0) =1/(2mu_0) ((B_0)/(sqrt2))^2=1/4 (B_0^2)/(mu_0)= 1/4((E_0//c)^2)/(mu_0)=1/(4mu_0) (E_0^2)/(c^2)=1/(4mu_0) (E_0^2)/((1//mu_0in_0))=1/4 in_0E_0^2=u_E`
`=2.21xx10^-10J//m^3`
(iii) Total average energy density of e.m. waves
`u=u_E+u_B=2.21xx10^-10+2.21xx10^-10=4.42xx10^-10J//m^3`