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.

Read more about this topic:  Dipole

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