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 = bar(U_(i)) - U_(f)= Kq_(1) q_(2) ((1)/(r_(0)) - (1)/(r_(f)))`
`= 9 xx 10^(9 ) xx ( 1-2 xx 10^(-12) ) ((100)/(2) - ( 100)/(5))`
`= 9 xx 12 xx30 xx 10^(-3)`
`= - 3.24 xx 10^(3) xx 10^(-3)`
`= - 3.24 J`
`W _( elec.) = ` negative
(ii) `W _( ext) = + 3.24 J, ` Positive
(iii) `U_(i) = 9 xx 10^(9) xx ( -12 xx 10^(-12)) xx ( 100)/(2) = - 5.4 J`
(iv) `U_(f) = 9 xx 10^(9) xx ( -12 xx 10^(-12)) xx ( 100)/( 5) = - 2.16 J`
(v) `U_(f) - U _(i) = - 2.16 - ( - 5.4) = 3.24 J`