Charges `+q` and `-q` are placed at points `A` and `B` respectively which are a distance `2L` apart, `C` is the midpoint between `A` and `B`. The work done in moving a charge `+Q` along the semicircle `CRD` is

Options

A. `(q Q)/(2pi in_(0) L)`
B. `(q Q)/(6pi in_(0) L)`
C. `(-q Q)/(6pi in_(0) L)`
D. `(q Q)/(4pi in_(0) L)`

Answer

C

Explanation

As is clear from Fig, `V_(C) = 0`,
`V_(D) = (q)/(4pi in_(0) (3L) - (q)/(4pi in_(0) L)) = (-q)/(6pi in_(0) L)`
`W_(CDR) = Q (V_(D) - V_(C)) = (-qQ)/(6pi in_(0) L)`