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## Homework Statement

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.

## Homework Equations

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?

thanks