Conducting sphere inside capacitor - QuickField simulation example
An uncharged conductive sphere is placed inside a charged parallel plate capacitor.
How to find conductive particle effect in capacitor dielectric?
Answer Typical applications Geometry
Given
Task
Solution
To model the conducting body with unknown potential we set the electric permittivity to a very high value (10000). This effectively makes the body's surface equipotential (as the real conductor' surface would be).
Results
Electric field distribution inside the dielectric:
Electric potential distribution inside the dielectric:
*Reference: Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207.
Engineering question
Set up a 3D QuickField Electrostatics problem for a conducting particle inside a capacitor dielectric and evaluate electric field distortion from computed field results.
capacitor dielectric inclusions, insulation defect sites, dielectric particle inclusions
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Simulation problem
Problem Type
Axisymmetric problem of electrostatics
Sphere radius: R = 1 mm;
Distance between the plates: d = 10 mm;
Dielectric permittivity: ε = 4;
Plate size: A = 100x100 mm²;
Voltage applied: V+ = 24 V.
Find the electric field stress in the dielectric.
To overcome 3D import limitations (only single body topology is allowed) we subtract the sphere from the dielectric body and import the resulting single body.
This problem could be simulated in 2D axisymmetric formulation if we replace square plates with discs of the same area (πD²/4 = A).
This modification preserves the inner field strength and the geometric capacitance values (~A/d).
Analytical solution:
External uniform electric field E0x = U / d = 24/10 = 2.4 [V/mm] = 2400 [V/m].
Electric potential outside the sphere U(x) = E0x * (R³/x² - x) [V] *
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