Electric Dipoles

located at position vector . We have seen that the electric field generated at point by an electric charge located at point is

(196) |

Hence, the electric field generated at point by an electric dipole of moment located at point is

(197) |

However, in the limit that ,

(198) |

Thus, the electric field due to the dipole becomes

(199) |

It follows from Equation (154) that the scalar electric potential due to the dipole is

(Here, is a gradient operator expressed in terms of the components of , but independent of the components of .) Finally, because electric fields are superposable, the electric potential due to a volume distribution of electric dipoles is

where is the