At a distance $d$ from a point charge $Q$, the energy density in its electric field is $u$. If we now go to a distance $d / 2$ from the charge, what is the energy density at the new location?

Question

Quizplus · Accepted Answer

The energy density $u$ in an electric field due to a point charge is proportional to the square of the electric field, which is inversely proportional to the square of the distance from the charge. Therefore, if the distance is halved, the energy density increases by a factor of $ (d/(d/2))^2 = 4^2 = 16 $.

At a Distance ddd From a Point Charge QQQ , the Energy Density in Its Electric Field Is

At a Distance $d$ From a Point Charge $Q$ , the Energy Density in Its Electric Field Is