Dipole Embedded in a Linear Dielectric Sphere

This Demonstration considers an electric dipole with dipole moment placed inside a sphere of radius composed of a linear dielectric material with dielectric constant .

Since there is no free charge, we can apply Gauss's law for the electric potential , which yields the Laplace equation

.

Imposing the appropriate boundary conditions (continuity of and discontinuity of ), it can be shown that the electric potentials inside and outside the sphere are given by

,

.

The corresponding electric field is given by . We plot this quantity to see the effect of different materials for the dielectric sphere. We consider the following media:

vacuum:

air:

silicon:

water:

ice: .

Reference

[1] D. J. Griffiths, Introduction to Electrodynamics, Boston: Pearson, 2013.