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Calculating Potential Outside the Sphere

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A point charge +q is situated a distance a (a>R)from the center of a grounded conducting sphere of radius R. Find the potential outside the sphere.

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Solution Summary

The potential outside a grounded conducting sphere is calculated.

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What is the method of images and what is it good for?

We all know that we can summarize the entire electrostatic theory in one equation, namely, the Poisson equation:

which satisfies some boundary conditions.
This equating, while seems innocent enough, can lead to some ugly calculations since it s a second-order non homogenous partial differential equation.

However, we can use the existence and uniqueness theorem that states that:
If there exists a solution to the Poisson equation that satisfies the boundary conditions, it is unique - it is the only possible solution.
How can we use this to our advantage?
If we can construct a simpler system than the original, that still satisfies the original boundary conditions, it will have the same solution to the Poisson equation. Hence, it will be electrostatic equivalent to the original system. Any electrostatic property of space (potential, fields, etc) will be identical in both systems.
The simplest electrostatic systems that we know are these that are composed ...

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