A system of three charges are placed as shown in the figure :

If `D gt gt d`, the potential energy of the system is :

Options

A. `(1)/(4piepsilon_(0))[-(q^(2))/(d)+(2qQd)/(D^(2))]`
B. `(1)/(4piepsilon_(0))[-(q^(2))/(d)-(2qQd)/(D^(2))]`
C. `(1)/(4piepsilon_(0))[+(q^(2))/(d)+(qQd)/(D^(2))]`
D. `(1)/(4piepsilon_(0))[-(q^(2))/(d)-(qQd)/(D^(2))]`

Answer

B

Explanation

`U=-(kq^(2))/(d)+(kqQ)/(D+(d)/(2))-(kqQ)/((D-(d)/(2)))`
`U=((-kq^(2))/(d)-(kqQd)/(D^(2)-(d^(2))/(4)))`
`Dgtgtgtd`
`U=((-kq^(2))/(d)-(kqQd)/(D^(2)))=(1)/(4piepsilon_(0))[-(q^(2))/(d)-(qQd)/(D^(2))]`