What minimum work must be done by an external force to bring a charge `q=3.00 muC` from a great distance away (take `t = infty`) to a point `0.500 m` from a charge ` = 20.0 muC` ?

Explanation

To find the work we cannot simply multiply the force times distance because the force is not constant. Instead we can set the change in potential energy equal to the (positive of the) work required of an external force `W= Delta U = (V_(b) - V_(a))`. We get the potentials `V_(b)` and `V_(a)` using `V= ( kQ)/( r )`
The work required is equal to the change in potential energy `:`
`W= q(V_(b)-V_(a))= q((kQ)/(r_(b))-(kQ)/(r_(a)))`
where `r_(b) = 0.500 m` and `r_(a) = infty` . The right hand term within the parentheses is zero `( (1)/(infty) =0)` so `W = ( 300 xx 10^(-5) C ) ((8.99 xx 10^(9) N.m^(2) //C^(2))(2.00 xx 10^(-5)C))/( ( 0.500m))= 1.08 J`