Capacitance of two unequal spheres

• peroAlex
In summary: This was very helpful. In my free time I did some extra experimentation. Thank you so much for your time and patience!
peroAlex
Assume that we have two charged spheres with unequal radii and which do not overlap. How cold we express their capacitance?

peroAlex said:
Assume that we have two charged spheres with unequal radii and which do not overlap. How cold we express their capacitance?
That's a pretty complex problem. What is the application? Is this a schoolwork problem? Do you have access to COMSOL or another modeling software package?

berkeman said:
That's a pretty complex problem. What is the application? Is this a schoolwork problem? Do you have access to COMSOL or another modeling software package?

Literary it's my curiosity at work. I know how to compute capacitance for system of two charged spheres with equal radius, but I never came across example of how two charged spheres with unequal radius.

How could we, for example, find such capacitance? I do have COMSOL.

To estimate it roughly, you can just draw a picture like this (each end of each line is orthogonal to the sphere):
,
then assign to each line a value of electric field, roughly equal to the voltage divided by the line's length;
then draw a rough diagram of the field on the big sphere, depending on the spherical angle,
multiplied by the electric constant, it's the charge distribution;
then, using some math, estimate the spherical integral and get the whole charge.
I did such estimations for similar problems, there was acceptable agreement with experiment.

Last edited:
peroAlex
peroAlex said:
How could we, for example, find such capacitance? I do have COMSOL.

In COMSOL it is almost trivial, it is just an electrostatic model. I believe there is a somewhat similar example in the manual.

peroAlex and berkeman
If you have the charge stored in the spheres you can find and vectorial equation for the electric field, right?
With this equation you can use numerical methods to evaluate the integral of electrical field through the line which is the smallest path between the spheres (a line) and evaluate the potential field difference (voltage).
The capacitance will be the charge of one of the spheres divided by the voltage between they.
Can someone point any mistake in my thoughts?

peroAlex
AlexCaledin said:
To estimate it roughly, you can just draw a picture like this (each end of each line is orthogonal to the sphere):
,
then assign to each line a value of electric field, roughly equal to the voltage divided by the line's length;
then draw a rough diagram of the field on the big sphere, depending on the spherical angle,
multiplied by the electric constant, it's the charge distribution;
then, using some math, estimate the spherical integral and get the whole charge.
I did such estimations for similar problems, there was acceptable agreement with experiment.

This was very helpful. In my free time I did some extra experimentation. Thank you so much for your time and patience!

1. What is capacitance?

Capacitance is the ability of a system to store an electric charge.

2. How is capacitance measured?

The unit of capacitance is the farad (F) and it is measured using a device called a capacitance meter.

3. What factors affect the capacitance of two unequal spheres?

The capacitance of two unequal spheres is affected by their size, distance between them, and the dielectric material between them.

4. How do you calculate the capacitance of two unequal spheres?

The capacitance of two unequal spheres can be calculated using the formula C = 4πεr/1/r1 - 1/r2, where ε is the permittivity of the dielectric material and r1 and r2 are the radii of the two spheres.

5. What is the significance of the capacitance of two unequal spheres?

The capacitance of two unequal spheres is an important factor in understanding the behavior of electrical circuits and systems, as it determines the amount of charge that can be stored and the strength of the electric field between the two spheres.

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