The configuration is that there is a charge +q a distance 3d on the z axis and a charge -2q a distance d on the z axis. The xy plane is a grounded conductor. Find the force on the charge +q.
I've place image charges: -q at z=-3d and +2q at z=-d.
the potential of the system is
V(r) = 1/4piepsilon [q/(x^2+y^2+(z-3d)^2)^0.5 -q/(x^2+y^2+(z+3d)^2)^0.5-2q/(x^2+Y^2+(z-d)^2)^0.5 + 2q/(x^2+Y^2+(z+d)^2)^0.5]
It think (sorry about the messy equation!
Force is just F=qE where E is the gradient of V(r).
The answer says that
F=q/4PIepsilon[ -2q/(2d)^2 +2q/(4d)^2 -q/(6d)^2 ]
How did they get that for the denominators in the brackets?