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

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Electrostatic Potential and Capacitance

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Potential due to a System of Charges

The electric potential at a point due to a system of point charges is equal to the algebraic sum of potentials due to all individual charges of the system at that point.

 

Consider a system of charges q1, q2,…, qn with position vectors r1, r2,…,rn relative to some origin. The potential V1 at P due to the charge q1, the potential V2 at P due to q2 and Vn due to qn are given by

straight V subscript 1 space equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q subscript 1 over straight r subscript 1 straight P end subscript
straight V subscript 2 space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q subscript 2 over straight r subscript 2 straight P end subscript
straight V subscript straight n space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q subscript straight n over straight r subscript nP

By the superposition principle,

V = V1 + V2 + ...Vn

straight V space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction open parentheses straight q subscript 1 over straight r subscript 1 straight P end subscript plus straight q subscript 2 over straight r subscript 2 straight P end subscript plus...... plus straight q subscript straight n over straight r subscript nP close parentheses

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