Capacitance of parallet plate with dielectric spheres in between

[amisha]

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

 

[edmondng]

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.

 

[Redbelly98]

This might be a situation where doing a measurement is much easier than doing the calculation.