Answer
61 km.
Work Step by Step
The energy per unit area per unit time is the magnitude of the average intensity, which we can relate to the electric field amplitude using equation 22–8. The intensity of the radio station at a given distance is assumed to be the radiated power, divided by the surface area of a sphere.
$$\overline{I}=\frac{P}{4\pi r^2}=\frac{1}{2}\epsilon_ocE_o^2$$
Solve for the radius.
$$r=\sqrt{\frac{P}{2\pi\epsilon_ocE_o^2 }}$$
$$r=\sqrt{\frac{25000W}{2\pi( 8.85\times10^{-12} C^2/(N\cdot m^2))(3.00\times10^8m/s)(0.020V/m)^2 }}$$
$$\approx 61\times10^{3} m$$