The energy density of the electric field generated by a point...

The electric field $E$ at a distance $r$ from a point charge $q$ is given by $E = \dfrac{1}{4\pi\epsilon_0}\dfrac{q}{r^2}$.

The energy density $u$ of an electric field is given by $u = \dfrac{1}{2}\epsilon_0 E^2$.

Substituting the expression for $E$, we get $u = \dfrac{1}{2}\epsilon_0 \left(\dfrac{1}{4\pi\epsilon_0}\dfrac{q}{r^2}\right)^2$.

This simplifies to $u = \dfrac{q^2}{32\pi^2\epsilon_0 r^4}$.

Thus, the energy density decreases with distance as $\dfrac{1}{r^4}.$