Question

A spherically-spreading EM wave comes from a 104.0 W source. At a distance of 9.6 m, what is the intensity of the wave?

Answer 1

Answer:

Approximately 0.0898 W/m².

Explanation:

The intensity of light measures the power that the light delivers per unit area.

The source in this question delivers a constant power of $\rm 104.0\; W$. If the source here is a point source, that $\rm 104.0\; W$ of power will be spread out evenly over a spherical surface that is centered at the point source. In this case, the radius of the surface will be 9.6 meters.

The surface area of a sphere of radius $r$ is equal to $4\pi r^{2}$. For the imaginary 9.6-meter sphere here, the surface area will be:

$\rm 4\pi \times (9.6\; m)^{2} \approx 1158.12\; m^{2}$.

That $\rm 104.0\; W$ power is spread out evenly over this 9.6-meter sphere. The power delivered per unit area will be:

$\displaystyle\rm  \frac{104.0\; W}{1158.12\; m^{2}}\approx 0.0898\; W\cdot m^{-2}$.