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# Physics/How to calculate the capacity of a metal plate ?

Question
Dear Sir,

I would like to evaluate the capacity “C”, of a metal plate, with the dimensions of :  axbxc, how can I find the capacity of a charged cube or prism, made of metal, with a certain length, width and thickness, it may be an approximate way of solution, what would you suggest ?

- I would like to suggest a way :
According the Gauss law, the electric field is the function of the charge and the charge is the function of the surface area, so
q = f(A), the bigger the area the more charge accumulated on the surface. In my solution, I calculate the whole area of the prism :
A = 2 x ((axb)+(bxc)+(axc)), and equalize the surface area to a hypothetical sphere with the same area, so A = 4 x pi x r^2, by this way I get the radius of an equivalent sphere as : r = (A/(4xpi))^(0.5), later, I calculate the C value, in a simple known way as,
C = 4 x pi x epsilon-zero x r, does this way make any sense ?

Yours Sincerely
Birol

Hello Birol,

Yes, your substitution of a sphere for a cube/prism is valid as an approximation - provided that the object is isolated from other objects by some distance much greater than a, b, or c.

Go to this site. Scroll up and down and compare the 2 cases discussed there. You can see how any nearby objects will affect the validity, even for an "isolated" sphere, of the formula
C = 4 x pi x epsilon-zero x r

I hope this helps,
Steve

Physics

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#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University