(a) Determine the electrostatic potential energy of a system consisting of two charge `7 muC and -2 muC` (and with no external field) placed at `(-9 cm, 0,0) and (9 cm, 0,0)` respectively.
(b) How much work is required to seperate the two charges infinitely away from each other ?
(c) Suppose that the same system of charges is now placed in an external electric field `E = A xx 1//r^(2)`, where `A = 9xx10^(5) C m^(-2)`.
What would the electrostatic energy of the configuration be ?

Explanation

(a) `U = (1)/(4pi epsilon_(0)) (q_(1)q_(2))/(r) =9 xx 10^(9) xx (7 xx (-2) xx 10^(-2))/(0.18) = 0.7 J`.
(b) `W = U_(2)-U_(1) = 0-U = 0 - (-0.7) = 0.7 J`.
(c) The mutual interaction energy of the two charges remains unchanged. In addition, there is the energy of interaction of the two charges with the external electric field. We find,
`q_(1)V(r_(1))+q_(2)V(r_(2)) = A (7 muC)/(0.09 m) + A(-2mu C)/(0.09 m)`
`q_(1)V(r_(1)) + q_(2)V(r_(2)) + (q_(1)q_(2))/(4pi epsilon_(0)r_(12)) = A(7mu C)/(0.09 m) + A (-2 mu c)/(0.09 m) - 0.7 J`
`= 70 -20 - 0.7 = 49.3 J`