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Electrostatic Potential and Capacitance

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Potential due to an Electric Dipole

An electric dipole consists of two equal and opposite charges q and –q separated by a (small) distance 2a. Its total charge is zero.

 

The potential due to the dipole is,

straight V space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction open parentheses straight q over straight r subscript 1 minus straight q over straight r subscript 2 close parentheses

Taking r1 and r2 = r2+ a2 ± 2arcosθ
r>>a

straight V space equals space fraction numerator straight p space cos space straight theta over denominator 4 space πε subscript 0 end fraction space
where p =2qa

Also comma space if space straight p space cos space straight theta space equals space bold p bold space bold. bold space bold r with bold hat on top bold space straight r greater than greater than straight a
straight V space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator bold p bold. bold r with bold hat on top over denominator straight r squared end fraction

(Positive sign for θ = 0, negative sign for θ = π.) The potential in the equatorial plane (θ = π/2) is zero.

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