The electric and magnetic fields in the charge free region in z>0 are given by:
\(\vec{E} = E_0 e^{-k_1 z} \cos (k_2 x -\omega t) \hat{j} \).
\(\vec{B} = \frac{E_0}{\omega} e^{-k_1 z} [k_1 \sin(k_2x- \omega t) \hat{i} + k_2 \cos(k_2 x- \omega t) \hat{k}] \).
where \(\omega , k_1 , k_2 \) are positive constants. The average energy flow in the x direction is?
1
\(\frac{E_0^2 k_2}{2 \mu_0 \omega} e^{-2 k_1 z} \)
2
\(\frac{E_0^2 k_2}{ \mu_0 \omega} e^{-2 k_1 z} \)
3
\(\frac{E_0^2 k_1 }{2 \mu_0 \omega} e^{-2 k_1 z} \)
4
\(\frac{1}{2} c ϵ_0 E_0^2 e^{-2 k_1 z} \)