(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^(-12)/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(-2 muC)/(0.09 m)` and the net electrostatic energy is `q_(1) V(r_(1)) + q_(2)V(r_(2)) + (q_(1)q_(2))/(4pi epsilonr_(12)) = A(7muC)/(0.09 m) + A(-2 muC)/(0.09 m) -0.7 J = 70-20-0.7 = 49.3 J`