An electric dipole moment
is placed in the center of a linear dielectric sphere of specified medium. The resulting potential and electric field inside and outside the sphere are plotted.
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:
 D. J. Griffiths, Introduction to Electrodynamics
, Boston: Pearson, 2013.