Electrostatic Potential and Capacitance

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Consider the two charges q₁ and q₂ initially at infinity and determine the work done by an external agency to bring the charges to the given locations.

Suppose, charge q₁ is brought from infinity to the point r₁. There is no external field against which work needs to be done, so work done in bringing q₁ from infinity to r₁ is zero. This charge produces a potential in space given by

The potential energy of a system of two charges

The potential energy of a system of 3 charges,