Question

show that the average energy density of the electric field equals the average energy density of the magnetic field in an em wav

Answer 1

we have to show that average energy density of the electric field = average energy density of the magnetic field

we know, average energy density in electric field , $U_E=\frac{1}{2}\epsilon_0E^2$......(1)

where, E is electric field intensity and $\epsilon_0$ is permittivity of medium.

and average energy density in magnetic field , $U_M=\frac{1}{2}\frac{B^2}{\mu_0}$........(2)

where B is magnetic field intensity and $\mu_0$ is permeability of medium.

also we know, $E=cB$ and $c^2=\frac{1}{\mu_0\epsilon_0}$, putting these in equations (1) and (2),

we get, $U_E=U_M$

hence, average energy density in electric field = average energy density in magnetic field .

Answer 2

Answer:

The average energy density of the Electric field(UE)

=

=

(as E=Bc)

=

o

=UB

Therefore the average energy density of the electric field is equal to the average energy density of the Magnetic field.