Electric Potential Energy two spheres connected by a long wire

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Two metal spheres, one larger (0.20 m radius) and one smaller (0.080 m radius), are connected by a wire, initially with zero charge. When a charge of 1.0 μC is placed on the larger sphere, it will redistribute between the two spheres to equalize the electrostatic potential. The charge on the smaller sphere can be calculated by ensuring the potentials at both surfaces are equal, using the formula for potential, kQ/R. The final potential at the surface of the smaller sphere will be the same as that of the larger sphere, and the unit of potential is joules per coulomb. Understanding these principles is crucial for solving the problem effectively.
Mikesgto
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Two metal spheres are connected by a long wire with a switch. The radius of the larger sphere (B) is b= 0.20 m and the radius of the smaller sphere (A) is a= 0.080 m. Initially the switch is open and both spheres have zero charge. Then charge Q0 = 1.0 μC is placed on the larger sphere.

B) Calculate the total electrostatic potential energy.
(c) Now close the switch. The system of two spheres will come to a new equilibrium. Calculate the equilibrium charge on the smaller sphere (A).
d)Calculate the final electrostatic potential at the surface of the smaller sphere (A).

Part A which included calculating the electrostatic potential at the surface of B was done by me. I attempted part be numerous times with the idea of splitting the charge up into 4 and then bringing them in one at a time, keeping in mind the way the charges would affect each other but that seemed to be wrong. I am completely lost with this one. Is the 1.0μC charge directly transferred to the smaller sphere?
 
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Is there no one that can someone shed some light on the subject? Just clear things up is all.
 
If connected, the surface of both spheres are at the same potential. For an isolated sphere, the potential on the surface is kQ/R. Assume that you can use this formula for the case when the spheres are connected with a wire. (It is a good approximation if they are far away from each other). The charge will be shared between them to make the potential equal on both spheres.

ehild
 
I thought the potential would be the same as well, but after I calculate the potential of the surface of the larger sphere, what charge should I use for the total? The answer I got for the surface potential of sphere B should be added to the surface potential of sphere A and that should be the total right?
 
Yes, the total charge is Q0 = 1.0 μC, and it is shared, so there is Qa charge on the smaller sphere and Qb=Q0-Qa on the bigger one, so as the potential is the same at both surfaces.

ehild
 
So wouldn't the "electrostatic potential at the surface of sphere B" be the same as A? I think the online homework expects an answer in joules which I don't really understand.
 
Mikesgto said:
So wouldn't the "electrostatic potential at the surface of sphere B" be the same as A? I think the online homework expects an answer in joules which I don't really understand.

The potentials are the same when the spheres are connected. And the unit of potential is joule/coulomb.

ehild
 
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