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

If `Dgtgtd`, the potential energy of the system is best given by :

Options

A. `1/(4pi epsilon_0)[-q^2/d-(q^Qd)/(2D^2)]`
B. `1/(4pi epsilon_0)[-q^2/d-(2q^Qd)/(D^2)]`
C. `1/(4pi epsilon_0)[-q^2/d-(q^Qd)/(D^2)]`
D. `1/(4pi epsilon_0)[-q^2/d-(q^Qd)/(D^2)]`

Answer

C

Explanation

`U_("system")=(1)/(4piepsilon_0)[((Qxxq))/(D+d//2)+(Q(-q))/((D-d//2))+(2xx(-q))/(d)]=(1)/(4piepsilon_0)[-(q^2)/(d)-(2qd)/(D^2)]" "(becauseD^(2)-(d^2)/(4)=D^(2))`