Potential Energy of a System of Charges | Electrostatic Potential and Capacitance | Notes | Summary - Zigya

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Electrostatic Potential and Capacitance

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Potential Energy of a System of Charges


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

straight V subscript 1 space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q subscript 1 over straight r subscript 1 straight P end subscript

The potential energy of a system of two charges

straight U space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r subscript 12 end fraction

The potential energy of a system of 3 charges,

straight U space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction open parentheses fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r subscript 12 end fraction space plus fraction numerator straight q subscript 1 straight q subscript 3 over denominator straight r subscript 13 end fraction space plus fraction numerator straight q subscript 2 straight q subscript 3 over denominator straight r subscript 23 end fraction close parentheses

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