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A completely isolated neutral conducting sphere of radius $R$ is kept such that its center is at a distance of $r\left(>R\right)$ from a point charge $+Q$.

How can I find the force of interaction of the induced charges and the point charge, or at least the energy? I can't use "method of images" because the sphere is not grounded.

Note: The actual question has a sphere already charged with $+Q$ charge and it asks for the $r$ at which the point charge is in equilibrium. I thought of breaking the force down into a superposition of two forces, one from the $+Q$ of sphere and the other from the induced charges. If there is some other way to solve this, I would like to know that too.

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You can always solve the Laplace equation in spherical co-ordinates(using Legendre polynomials,etc).But even method of images will work.We have to use two image charges instead of one. –  Sandesh Kalantre Jan 24 at 12:36

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