Dipole - Field From An Electric Dipole

Field From An Electric Dipole

The electrostatic potential at position r due to an electric dipole at the origin is given by:

where

is a unit vector in the direction of r', p is the (vector) dipole moment, and ε₀ is the permittivity of free space.

This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential Φ(r). If the source of Φ(r) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ(r). The electric field from a dipole can be found from the gradient of this potential:

where E is the electric field and δ3 is the 3-dimensional delta function. This is formally identical to the magnetic H field of a point magnetic dipole with only a few names changed.