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Question
The energy density in the electric field created by a point charge falls off with the distance from the point charge as
Options
`1/r`
`1/r^2`
`1/r^3`
`1/r^4`
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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`
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