#### Question

The energy density in the electric field created by a point charge falls off with the distance from the point charge as

`1/r`

`1/r^2`

`1/r^3`

`1/r^4`

#### Solution

`1/r^4`

Energy density U is given by `U = 1/2∈_0E^2`.......(1)

The electric field created by a point charge at a distance r is given by `E = q/(4pi∈_0r^2)`

On putting the above form of E in eq. 1, we get

`U = 1/2 ∈_0(q/(4pi∈_0r_2))^2`

Thus, U is directly proportional to `1/r^4`

Is there an error in this question or solution?

Solution P the Energy Density in the Electric Field Created by a Point Charge Falls off with the Distance from the Point Charge as Concept: Energy Stored in a Capacitor.