When a negative charge is taken at height from earth earth surface then it's potential energy

imagine the earth to be a neutral body….

as soon as one takes a charge -q from earth….

the earth gets a +q charge.

now if you carry it to a height say h from earth surface you are doing work against the force acting towards earth.

if the force is F(r) , then , F= k q^2 /r^2

F.dr is the work done in moving from r to r+dr

an integral of F.dr between R and R+h can give us the amount of work done

W = { integ F.dr } = {integ (k q^2 /r^2).dr } limits R and R+ h

W = k.q^2 { -1/r} = k.q^2 { 1/R - 1/ (R+ h) }