Two charges `q_(1) = 3.0 mu C` and `q_(2) = - 4.0 mu C` initiallly are separated by a distance `r_(0) = 2.0 cm `. An external agent moves the charges until they are `r_(f) = 5.0 cm ` apart.
(i) How much work is done by the electric field in moving the charges from `r_(0) ` to `r_(f)` ? Is the work positive or negative ?
(ii) How much work is donw by the external aganet in moving the charges from `r_(0)` to `r_(f)` ? Is the work positive or negative ?
(iii) What is the positive energy of the initial state where the charge are `r_(0) =2.0` cm apart ?
(iv) What is the potential energy of the final state where the charges are `r_(f)= 5.0cm` apart ?
(v) What is the change in potential energy from the initial state to the final state ?

Explanation

(i) `W_("elec")=-DeltaU=U_(i)-U_(f)=Kq_(1)q_(2)((1)/(r_(0))-(1)/(r_(1)))`
`= 9xx10^(9)xx(-12xx10^(-12))((100)/(2)-(100)/(5))`
`=-9xx12xx30xx10^(-3)`
`=-3.24xx10^(3)xx10^(-3)`
`=-3.24` J
`W_("elec")= `negative .
(ii) `W_("ext")= +3.24J , ` Positive
(iii) `U_(i)= 9xx10^(9)xx(-12xx10^(-12))xx(100)/(2)=-5.4` J
(iv) ` U_(i) = 9xx10^(9)xx(-12xx10^(-12))xx(100)/(5)=-2.16 J`
(V) `U_(t)-U_(i)=-2.16-(-5.4)= 3.24` J