Capacitance of parallet plate with dielectric spheres in between

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SUMMARY

The discussion focuses on calculating the capacitance of a parallel plate capacitor with dielectric spheres of varying radii and dielectric strengths positioned between the plates. The capacitance formula is defined as C = permittivity × dielectric × area / distance. The integration of capacitance for spheres is emphasized, noting that the dielectric distance varies depending on the sphere's position. A practical approach is suggested, using square dielectrics arranged in series and parallel configurations to simplify measurements.

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  • Understanding of capacitance and its mathematical derivation
  • Familiarity with dielectric materials and their properties
  • Knowledge of integration techniques for varying geometries
  • Basic circuit theory, specifically series and parallel configurations
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  • Study the mathematical derivation of capacitance for different geometries
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Electrical engineers, physics students, and professionals involved in capacitor design and analysis will benefit from this discussion.

amisha
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I want to calculate the capacitance of a system consisting a parallel plate and dielectric spheres of different radius and dielectric strength in between the plates.
please give some mathematical derivation.
I really need to know it,my career depends on it.
Please help me.
:)
thanks & regards
ruhi
 
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capacitance in parallel is same as resistor in series and vice versa.
c = permittivity*dielectric*area/distance

If you have a sphere, it will be an integration of series of capacitance depending on the diameter of the sphere at different location. At the tip of the sphere, the dielectric distance/space is less compared to the middle of the sphere. For example if you had a circle, the diameter maybe say 1m, but it is not 1m x 1m. Instead it is 1m diameter but as you cut and move along the circle, it becomes 0.99m,0.98m,0.979999m etc.

For start, i suggest using a square dielectric. Take 3 squares, with 2 of them being the same length but 1/2 the length of the first one. Put the 2 smaller square in series (next to each other). Stack the bigger square on top of them. The circuit will look just like 2 resistor in series parallel with the other.
 
This might be a situation where doing a measurement is much easier than doing the calculation.
 

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