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

Answer

C

Explanation

`U_("system")=(1)/(4 pi epsilon_(0))[((Qxxq))/(D+d//2)+(Q(-q))/((D-d//2))+(2xx(-q))/(d)]`
`=(1)/(4 pi epsilon_(0))[-(q^(2))/(d)-(2qd)/(D^(2))] " "( :' D^(2)-(d^(2))/(4)=D^(2))`