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:
vacuum:
air:
silicon:
water:
ice: .
Reference
[1] D. J. Griffiths, Introduction to Electrodynamics, Boston: Pearson, 2013.