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In an electromagnetic wave, the amplitud...

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.

Text Solution

Verified by Experts

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`
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Knowledge Check

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