1.

Show that the average energy density of the electric field `vecE` equals the average energy density of the magnetic field `vecB`, in electromagnetic waves.

Answer» Average energy density of electric field is given
by,
`u_E=1/2in_0E_(rms)^2=1/2in_0((E_0)/(sqrt2))^2=1/4in_0E_0^2....(i)`
Average energy density of magnetic field is given by,
`u_B=1/(2mu_0) B_(rms)^2 =1/(2mu_0)((B_0)/(sqrt2))^2=1/4 (B_0^2)/(mu_0).....(ii)`
We know `E_0=cB_0 or B_0 =E_0//c`
Also `c=1/sqrt(mu_0in_0)`
Putting values in (ii) , we get
`u_B= 1/(4mu_0) (E_0^2)/(c^2) =1/(4mu_0) (E_0^2)xxmu_0 in_0=1/4 in_0E_0^2=u_E`


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