Which of the following statements is correct regarding the energy density $u$ of an electromagnetic wave in vacuum?

Solution

1. The total energy density $u$ of an electromagnetic wave is the sum of the electric energy density $u_E=\frac{1}{2}{ϵ}_0{E}^2$ and the magnetic energy density $u_B=\frac{B^2}{2{\mu }_0}$.
2. Using the relationship $E=cB$ and the identity $c^2=\frac{1}{{\mu }_0{ϵ}_0}$, we can substitute $E$ into the expression for $u_E$.
3. This substitution yields $$\begin{array}{rl}{u}_E& =\frac{1}{2}{ϵ}_0(cB{)}^2\\ & =\frac{1}{2}{ϵ}_0(\frac{1}{{\mu }_0{ϵ}_0})B^2\\ & =\frac{B^2}{2{\mu }_0}\end{array}$$, which is equal to $u_B$.
4. Since $u_E=u_B$, the energy is equally divided between the electric and magnetic fields.
5. Hence the answer is (C).