Dielectric Sphere in a Uniform Electric Field
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration shows the electric field in and around a spherical dielectric in a uniform external electric field. The spatial distribution of field intensity and direction are indicated by colors and arrows, respectively. You can vary the relative permittivity of the sphere and the surrounding medium. In the graphics, the radial and axial lengths are normalized to the sphere radius , and the field intensity magnitude is given relative to the applied field .
Contributed by: Y. Shibuya (January 2013)
Open content licensed under CC BY-NC-SA
Snapshot 1: dielectric sphere with a larger permittivity ()
Snapshot 2: sphere with infinite permittivity (), equivalent to a conducting sphere
Snapshot 3: sphere with smaller permittivity (), representing a void in the dielectric
The electric field can be obtained from as shown below.
Since the remaining components are zero, the above vectors are displayed as two-dimensional graphics in the - plane. The field inside the sphere is uniform, its value being less than for . However, it is greater than for , as seen in snapshot 3. In the extreme case of , it tends to 1.5 . Outside the sphere, the maximum field 3 occurs at for (snapshot 2).
 J. D. Jackson, Classical Electrodynamics, 3rd ed., New York: Wiley, 1999.