# Power Density Function

A radio receiver needs $1 \textrm{ nW}/\textrm{m}^2$ of power density function, how far away from a 1-watt point source will it continue to work?

So how do we calculate power density? We simply take the formula for the surface of a sphere, $$P_s=4 \pi r^2$$ Next, we spread out our 1 watt over that surface, so we have density of $$P_d=\frac{P_{Tx}}{P_s}=\frac{1\mbox{ }W}{4 \pi r^2}$$ Our problem says that $P_d=\frac{1\mbox{ } nW}{m^2}$, so we just need to solve the equation for $r$ to get the final solution.