You are moving a negative charge `q lt 0` at a small constant speed away from a uniformly charged non-conducting spherical shell on which resides a negative charge `Q lt 0`. The electrostatic, field of `Q` is `E`. Let `U` be the total energy of the system, `W_(a)` the work done by the force `F_(a)` you exert on `q, W_(E)` the work done by the electrostaitc force `F_(E)` on `q`. Then, as `q` is being moved :

Options

A. `W_(a) = - W_(E)`, therefore `U` remains constant
B. `F_(a) = - F_(E)`
C. `U` increases
D. `U` decreases

Answer

D

Explanation

If charge is being moved slowly, `vecF_(a) = - vecF_(E)`
`W_(a) + W_(E) = DeltaKE = 0` [charge is moved slowly]
i.e `W_(a) = W_(E)` also `W_(E) = - 4Delta` thus `W_(a) = +4U`
As force `F_(a)` and displacement are `180^(@)`,
`vecF d vecr lt 0` or `W_(A) lt 0` thus `DeltaU lt 0`
Therefore `U` decreases.