How Do You Calculate Capacitance Between Two Spherical Conductors?

[Brewer]

Question asks:

Two spherical conductors of radius 0.01m are placed with their centres 0.1m apart. Calculate the capacitance (C) of this system.

I can't do it like a parallel plate capacitor can i? and its not a traditional spherical capacitor is it? So I'm going to have to do it the long boring way, by finding the electric field between the two, and using that to find the potential difference between them aren't I?

Please tell me there's a quicker way than this!

 

[pizzasky]

Q = CV, but do you know another equation for V, one that involves charge and distance perhaps?

Edit (in reply to post #3): My apologies, I guess I forgot about the part about point charges.

 

[Brewer]

V=kQ/r?

But isn't that for point charges, of which this isn't?

 

[arunbg]

Brewer there is no quicker way. It is given as a standard result in many texts.

 

[Brewer]

balls!

I have read the question correctly and that the spheres are next to each other rather than a sphere inside a sphere?

Its just I can't find examples of the next to each other case, but loads for sphere in a sphere.

 

[Brewer]

Right, I get an answer of:
$$C = \frac{ \epslion_{0}4\pi(r_{a}+r)r_{a}}{r}$$

which when I plug the numbers in gives me $$1.22*10^{-12} F$$

where $$r_{a}$$ is the radius of a sphere, and r is separation between them.