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Electrostatic Potential And Capacitance

Question

Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).

Solution

Potential at P, due to charge +q at A

= \frac{1}{4 {πε}_{0}} \frac{q}{r + a}

Potential at P, due to charge -2q at B

= \frac{1}{4 {πε}_{0}} \frac{- 2 q}{r}

Potential at P, due to charge +q at C

= \frac{1}{4 {πε}_{0}} \frac{q}{r - a}

Total electrostatic potential at P