(a) Determine the electrostatic potential energy of a system consisting of two charge `7 muC and -2 muC` (and with no external filed) placed at `(-9 cm, 0,0) and (9 cm, 0,0)` respectively.
(b) How much work is required to separate 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 = (q_(1) q_(2))/(4pi in_(0) r)`
`7xx10^(-6)xx(-2xx10^(-6)xx9xx10^(9))/((9+9)xx10^(-2)) `
= 0.7 J
(b) Work required `= U_(2) - U_(1) = 0 - U = 0.7 J`
(c ) In the electric field, total P.E
`= (q_(1) q_(2))/(4pi in_(0) r)+ q_(1) V vec((r_(1))) + q_(2) V vec((r_(2))`
From `E = (-dv)/(dr)` ,
`V = int -Edr = int - (A)/(r^(2)) dr = (A)/(r)`
`:.` Total `P.E. = (q_(1) q_(2))/(4pi in_(0) r) + (A q_(1))/(r_(1)) + (Aq_(1))/(r_(1)) + (Aq_(2))/(r_(2))`
`(-0.7) + (9xx10^(5) (7xx10^(-6))/(0.09)`
`+ (9xx10^(5) (-2xx10^(-6))/(0.09)`
`= -0.7+70-20 = 49.3 J`