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 = `DeltaU = q( V_(b)-V_(a))` . We get the potentials `V_(b)` and `V_(a) ` using `V=(kQ)/(r )`
The 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)=oo` . The right hand term within the parentheses is zero `((1)/(oo)=0)` so
`W=(300xx10^(-6)C)((8.99xx10^(9)N.m^(2)//C^(2))(2.00xx10^(-6)C))/((0.500m))=1.08 `J.