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. `(qQ)/(4 pi epsilon_(0) L)`
B. `(qQ)/(2 pi epsilon_(0) L)`
C. `(qQ)/(6 pi epsilon_(0) L)`
D. `-(qQ)/(6 pi epsilon L)`

Answer

4

Explanation

`V_(C ) = 0 , V_(D) = (1)/(4 pi in_(0)) [ (q)/(3L) + (-q)/(L)] = -(1)/(4 pi in_(0)) .(2q)/(3L)`
`W_(CrarrD) = Q(V_(D) - V_(C )) = -(1)/(4 pi in_(0)) .(2qQ)/(3L)`
`= -(qQ)/(6 pi in_(0) L)`