Potential Due to an Electric Dipole

The potential at a point due to a dipole is obtained by adding the potentials due to the two charges using the principle of superposition.

For a point far from the dipole, the dipole behaves differently from a single point charge: the potential depends on both the distance from the dipole and the angular position of the point.

An electric dipole is a pair of equal and opposite charges separated by a small distance.

If the charges are separated by a distance 2a2a, then 2a2a is called the dipole length.

\[V=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{p\cos\theta}{r^{2}}=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{\vec{p}\cdot\vec{r}}{r^{3}}(r>>a)\]

The electric dipole moment is:

\[\vec{p}=q(2a)\hat{p}\]

Its direction is from the negative charge to the positive charge.

Quick Interpretation

• Potential is maximum positive on the side of the positive end of the dipole.
• The potential is zero along the equatorial line because the contributions from the two charges cancel.
• Potential becomes negative on the opposite axial side.

Many molecules, such as water, are polar in nature and behave like electric dipoles. The idea of dipole moment helps explain how such molecules interact with electric fields.

Simple Analogy

A dipole is like two opposite “electric influences” placed very close together. Far away from them, their combined effect does not vanish completely, but it weakens faster than that of a single charge.