Capacitance of two spherical conductors

[funkwort]

Given that two spherical conductors of radii r1 and r2 are separated by
x>>(both r), connected by a thin wire, and charged with 7 uC - how is the charge distributed between the spheres (no charge on wire)?

I tried using charge density but:

Qtot/A1+A2 = Q1/A1 + Q/A2 doesn't work by definition

then maybe:

C(dV) = Q for either sphere - but how do you find dV without knowing the charge on each first? However, I got the correct answers when I flukily got dV by using the total charge of the system (7uC) and the sum of the radii (r1+r2) and multiplying by C of each sphere. I don't understand why this worked though.

 

[dextercioby]

Well,i don't follow your "proof".I would advise you to use the fact that the charges on the 2 spheres are distributed in such a way,as to insure equal electric potential for each sphere...

Daniel.

 

[funkwort]

why do they have to have the same electric potential?

 

[dextercioby]

Because if they didn't charge would be moving from one to another until they did.So better assume that they already do.

Daniel.

 

[funkwort]

ok, I see. This means that the potential difference between them is 0 right? Also, would the potential of the system be V1 + V2?

 

[dextercioby]

Yes to the first question...As for the second,you don't need that piece of information.

Daniel.

 

[funkwort]

Ok, but what if I wanted to know the potential of the system - would it be V1 + V2?

 

[dextercioby]

Yes,potential (electric) is additive.But,again,you don't need this info.

Daniel.