Two Conducting Spheres connected by a wire

1. The problem statement, all variables and given/known data

Two conducting spheres of radii rA and rB are connected by a very long conductive wire. The charge on sphere A is Qa and rA < rB.

What is the charge on sphere B?

Which sphere has the greater electric field strength immediately above its surface.

2. Relevant equations
Esurface = [itex]\eta[/itex]/[itex]\epsilon[/itex]naught

3. The attempt at a solution

So I assume that any charge placed on the two conductors will reach an equilibrium which I assume would mean that both conductors have the same surface charge density.

That is:


However, when I solve for Qb, I get (rB/rA)^2*Qa which is incorrect. The correct answer is apparently (rB/rA)*Qa.

For the second question, I need to find the electric field strength at the surface of each conducting sphere. Well since I assumed that the surface charge density was the same, using the equation listed above, I should have equivalent electric field strengths. Instead, the answer states that the electric field strength on sphere A is greater than that of B. Why?

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