Surface charge distribution of two metal spheres

[jdstokes]

Homework Statement

A total charge Q is shared by two metal spheres of small radii R1 and R2, that are connected by a long thin wire of length L. Fin (a) the charge on each sphre and (b) the tension in the wire.

Source: Haliday 4th edn chapter 26 q. 91, p. 738

The Attempt at a Solution

I'm a bit confused by this. I assume that since the potential must be uniform for a conductor, that we can make the equation

$\frac{rQ}{4\pi\epsilon_0 R_1} = \frac{(1-r)Q}{4\pi\epsilon_0 R_2}$

from which we obtain

$Q_1 = \frac{Q}{1 + R_2/R_1}$.

But I suppose this is only valid if the length of L is sufficiently large that we can ignore the interaction energy of the two spheres right?

 

[jdstokes]

Perhaps I am correct, and merely

$\mathrm{Tension} = \frac{Q_1 Q_2}{4\pi \epsilon_0 (L + R_1 +R_2)^2}$?

 

[Redbelly98]

You're correct for both parts.

However, they probably want tension in terms of the given parameter Q, not in terms of Q₁ and Q₂.