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Electric potential due to electric dipole

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Write down an expression for the electric potential about an electric dipole, as a function of the spatial coordinates relative to the dipole.

Calculate the electric field as a function of these spatial coordinates from the electric potential.

A 2D solution (with the dipole existing in the 2D plane) is fine.

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Solution Preview

Let us consider the potential at a point P with coordinates (r, θ) as shown.

The potential at a point due to a charge q is kq/r, where k = 1/(4Πε0) = 9 x 109.

r1 ≈ r - a(cos θ)

r2 ≈ r + a(cos θ)

The potential at P due to the charge +q is ...

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