In a plane e.m.wave, the electric field oscillates sinusoidally at a frequency `2xx10^10Hz` and amplitude `45Vm^-1`.
(a) What is the wavelength of wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the electric field `vecE` equals to the average energy density of the magnetic field `vecB`.

Answer

(a) `1.5xx10^-2m (b) 1.5xx10^-7T`

Explanation

(a) `lambda=c//v=3xx10^8//2xx10^(10)=1.5xx10^-2m`
(b) `B_0=E_0//c=45//(3xx10^8)=15xx10^-8T`
(c) Energy density in electric field,
`u_E=1/2 in_0E^2`
and energy density in magnetic field,
`u_B=1/(2mu_0)B^2`
Now, `u_E=1/2 in_0E^2=u_E=1/2 in_0(cB)^2`
`=1/2 in_0c^2B^2`
`=1/2 in_0 1/(mu_0in_0)B^2=1/(2mu_0)B^2=u_B`.
Hence, `u_E=u_B`