# Electric Potential and Spheres

Two unequally sized metal spheres are each charged. A wire is connected from one sphere to the other. When the wire is removed, the spheres will have the same potential. T/F?

The answer is true (I looked up the key), but I do not understand why.

I know that the spheres, due to being unequally sized, have different charges. But I thought potential was EPE/q, which is (Qq/r)/q, which simplifies to Q/r. If the spheres have different charges, won't the potential always be different? Can someone help explain why the potentials would be the same?

Thanks!

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The spheres have the same potential because there can't be an electric field in the wire if the charges are in equilibrium and no current flows.

This means that the charge must distribute itself in such a way that the potential on the spheres is the same.

The potential of a sphere with radius r and charge Q is. $$\frac{Q}{4 \pi \epsilon_0 r}$$

obviously Q depends on r

The spheres have the same potential because there can't be an electric field in the wire if the charges are in equilibrium and no current flows.

This means that the charge must distribute itself in such a way that the potential on the spheres is the same.

The potential of a sphere with radius r and charge Q is. $$\frac{Q}{4 \pi \epsilon_0 r}$$

obviously Q depends on r
OK, you explanation makes sense--there can be no potential difference because of the way the charges move. When they say potential, though, what do they mean? Because the charge Q is different for each of the spheres, clearly they don't mean the potential as from a distance R--if the Q's are different, and R is the same, the clearly Q1/R != Q2/R.

Sorry if my follow-up question is vague, I'm finding it hard to phrase.

they're unequally sized spheres, so R is NOT the same

Ah, I was thinking of R as the distance away from the spheres, not the radius of the spheres. I'm doing AP Physics B, so we don't really do very much with the potential of spheres, since it's a C subject. Please excuse me!