Charge Transfer from sphere to sphere

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AI Thread Summary
A metal sphere with a charge of 6nC is connected via a wire to a neutral sphere with double its diameter. Charge will flow until both spheres reach the same electric potential, resulting in a uniform surface charge distribution. The final charge on the larger sphere is calculated to be four times that of the smaller sphere, but the textbook states it should be two times. The potential at the surface of each sphere must be equal for equilibrium, leading to the conclusion that charge distribution is dependent on their sizes. The discussion emphasizes the importance of understanding electric potential and charge conservation in this scenario.
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Homework Statement


There is a metal sphere charged to 6nC. A wire then connects this sphere to another sphere which has 2x the diameter and neutral. What are the final charges on each sphere?


Homework Equations





The Attempt at a Solution


I think the idea behind this is that the charge will flow from the charged sphere to the neutral one until the neutral one has gained enough charge that there's no longer a voltage difference. However I don't know how to get voltage difference in this situation.
Instead, I solved using the idea that the final surface charge distributions of both spheres should be the same.

So I did something like this,

Q1/r2=Q2/(2r)2 (the 4pi cancels out)
from this I get the charge on the larger ball has to be 4x that of the smaller ball, however in my textbook it says the larger ball has 2x the charge.
 
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Write up the potential at both surfaces with respect to infinity. They have to be equal, otherwise charge will flow from the higher potential to the lower one. If the spheres are far enough the surface charge distribution is homogeneous. The potential of a sphere is the same as that or a point charge in the centre.

ehild
 
What is the electric potential at the surface of a sphere of radius, R, and charge Q?

V(R) = k\frac{Q}{R}

Yes, the potential difference is zero.

V(R)-V(2R)=0

Use a charge of Q1on one sphere, Q2 on the other. Q1+Q2 = QTotal.
 
ok thanks guys
 
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