Two charges of equal magnitude q are placed in air at a distance 2a apart and third charge `-2q` is placed at mid-point . The potential energy of the system is `(epsi_(0)` = permittivity of free space)

Options

A. `-(q^(2))/(8pi epsilon_(0)a)`
B. `-(3q^(2))/(8pi epsilon_(0)a)`
C. `-(5p^(2))/(8pi epsilon_(0)a)`
D. `-(7q^(2))/(8pi epsilon_(0)a)`

Answer

D

Explanation

Potential energy of the system,

`U=(1)/(4pi epsilon_(0))[(q_(1)q_(2))/(r_(12))+(q_(1)q_(3))/(q_(13))+(q_(2)q_(3))/(r_(23))]`
`=(1)/(4pi epsilon_(0))[(q(-2q))/(a)+(q(-2q))/(a)+(qq)/(2a)]`
`=(1)/(4piepsilon_(0))[-(2q^(2))/(a)-(2q^(2))/(a)+(q^(2))/(2a)]`
`=(1)/(4pi epsilon_(0))[(-4q^(2))/(a)+(q^(2))/(2a)]=(-7q^(2))/(8pi epsilon_(0)a)`