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

Answer

D

Explanation

In Ist case, when charge + Q is situated at C

Electric potential energy of system
In Iind case When charge `+ Q` is moved from C to d

Electric potential energy of system in this case
`U_(2)=(1)(4piepsilon_(0))(q(-q))/(2L)+(1)/(4pieplsilon_(0))(qO)/(3L)-(1)/((4pieplsilon_(0))(q0)/(L))`
`=(qQ)/(4piepsilon_(0))[(1)/(3L)-(1)/(L)]=(qQ)/(4piepsilon_(0))(1-3)/(3L)=-(2qQ)/(12piepsilon_(0)L)=-(qQ)/(6piepsilonL)`