Answer
$E_o=\sqrt{\frac{\mu_ocP_0}{2\pi r^2}}$.
Work Step by Step
The light emits equally in all directions, so the intensity at a given distance is the radiated power, divided by the surface area of a sphere. Relate the electric field amplitude to the average intensity, using equation 22–8.
$$\overline{I}=\frac{P_0}{4\pi r^2}=\frac{1}{2}\epsilon_ocE_o^2$$
Use equation 22–3 to relate the permittivity of free space to the permeability.
$$\frac{1}{2}\epsilon_ocE_o^2=\frac{1}{2}(\frac{1}{c^2\mu_o})cE_o^2$$
Combine the above equations.
$$\frac{P_0}{4\pi r^2}=\frac{1}{2}(\frac{1}{c\mu_o})E_o^2$$
Solve for the electric field amplitude.
$$E_o=\sqrt{\frac{\mu_ocP_0}{2\pi r^2}}$$
This was the relationship to be proven.
