Dielectric sphere in a uniform electric field - QuickField simulation example
The dielectric sphere is submerged into the uniform electric field.
How to find electric field in dielectric spheres?
Engineering answer Typical applications Geometry
Given
Task
Solution
In QuickField to simulate uniform external electric field we apply 0 and +10 kV on two faces separated by 1 meter distance. Ther problem can be simulated both in 2D and in 3D.
Results
Electric field distribution inside and outside the dielectric sphere (2D and 3D):
Reference:
Engineering question
Set up a 3D QuickField Electrostatics problem for a dielectric sphere and evaluate electric field distribution from computed field results.
dielectric inclusion materials, composite insulation systems, embedded dielectric particles
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Simulation problem
Problem Type
3D-import electrostatics.
Sphere diameter d = 50 mm
Relative permittivity of dielectric ε = 4,
External field strength E0 = 10 kV/m.
Find the electric field distribution inside the sphere.
Analytical solution [1, page 115] gives the average electric field stress inside the sphere: E = E0 * 3/(2 + ε)
Analytical solution: E = 10 * 3/(2 + 4) = 5 kV/m = 5000 V/m (average in a volume)
QuickField 2D: E = 5002 V/m (center of the sphere)
QuickField 3D: E = 5026 V/m (center of the sphere)
[1] J.Jackson. Classical Electrodynamics. 3-d edition. Hoboken, NJ, USA: John Wiley & Sons, 1998.
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