How Do Three Connected Conducting Spheres Share Total Charge?

[mitleid]

Was curious how some of you guys would solve this problem...

Three conducting spheres of radii a, b and c are connected by negligibly thin conducting wires. Distances between the spheres are much larger than their sizes. The electric field on the surface of a is measured to be E_{a}. What is the total charge Q that this system of three spheres holds?

E = Q/r^{2}*Ke

Q = Q_{a}+Q_{b}+Q_{c}

The way I solved it is most likely not the way my professor intended. I said that since the amount of charge on each sphere is a function only of the radius of the sphere...

a + b + c = x

a/x = percentage of Q shared on sphere a (called this S_{a})

so Q_{a} = S_{a}*Q
and Q = Q_{a}/S_{a}

I imagine I'm missing a conceptual link that'd make another path to solving this more clear.

 

[Astronuc]

The charge surface density would equal, so the total Q is distributed according to the fraction of surface area.

Determine the surface area for each sphere and total of all three, then ratio the area of each sphere to the total.

Area of sphere is proprotional to r², where r is the radius.