Chapter 7, Problem 41P

Given a wave with $E=\hat{x}$ E₀ cos(ωt − kz):

1. (a) Calculate the time-average electric energy density

${(w_e)}_{av}=\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int }}{w}_{e}dt\text{}=\frac{1}{2T}}{\displaystyle \underset{0}{\overset{T}{\int }}ϵE^2}dt$.

1. (b) Calculate the time-average magnetic energy density

${(w_{\text{m}})}_{\text{av}}=\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int }}{w}_{\text{m}}dt\text{}=\frac{1}{2T}}{\displaystyle \underset{0}{\overset{T}{\int }}\mu H^2}dt$.

1. (c) Show that (w_e)_av = (w_m)_av.