A point light source emits E.M. waves in free space. A detector,...

For a point light source, the intensity of electromagnetic waves at a distance $r$ is given by $I = \dfrac{P}{4\pi r^2}$, where $P$ is the power of the source.

Since the detector is moved to a new location on the same spherical surface, the distance from the source remains $L$.

The emission from a point source is isotropic, meaning the intensity depends only on the radial distance from the source and is independent of the angular position.

Therefore, the intensity at the new location remains unchanged, which is $I_o$.

Answer: $I_o$