Electric Potential Energy two spheres connected by a long wire

[Mikesgto]

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?

 

[Mikesgto]

Is there no one that can someone shed some light on the subject? Just clear things up is all.

 

[ehild]

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

 

[Mikesgto]

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?

 

[ehild]

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

 

[Mikesgto]

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.

 

[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.

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

ehild