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

Answer

C

Explanation

Work done in charging capacitor

Possiional at point `C= (kq)/(L)- (kq)/(L)= 0`
Possential at point `D= (kq)/(3L)- (kq)/(L)`
`=(kq- 3kq)/(3L)= (-2kq)/(3L)`
Work done in moving a charge +Q along the semicircle CRD - 3U
`= _Q (V_(D)- V_(C ))`
`=+Q ((-2kq)/(3L)- 0)`
`rArr (-2kQq)/(3L) = -2 xx (1)/(4pi epsi_(0)) xx (Qq)/(3L)`
`rArr (-Qq)/(6pi epsi_(0) L)`