Why they have the same potential?

[bethny10]

Here's my problem:
Two conducting spheres, one having twice the diameter of the other, are separated by a distance large compared to their diameters. The smaller sphere (1) has a charge of q and the larger sphere (2) is uncharged. If the spheres are connected by a long thin wire:

And, here's the right answer:
1 and 2 have the same potential

Here are the wrong answers:
2 has half the potential of 1
2 has twice the potential as 1
1 and 2 have the same charge <--(my choice)
all of the charge is dissipated

I know the right answer (because it was given to me) but i don't know WHY, and i'd like to get an answer...can anyone help me?

i'm kind of "slow" at understanding concpets, so the simpler this can be put, the more greatly appreciated it will be!

 

[lightgrav]

They're connected by a wire, which is a conductor.

They started out at different Electric Potential, so there used to be
an Electric field between them (dV = E . dx).
Electric charges move through the connecting wire until dV = 0.

 

[phucnv87]

When two or more conducting objects are conneted by wire, they will have the same potential after a long time .
This is so obvious because then there's no charge flowing through the wire.

 

[bethny10]

So, are the spheres like a fully charged capacitor that's been hooked up to a battery for a long time?
b/c in that case the capacitor will have the same change in V as the V of the battery, so the two spheres attached to each other will have the same V.
Am I right?

 

[lightgrav]

more important, the wire that connects the spheres is like
the wires that connect battery terminal to capacitor plate.

Careful with your wording : It is the DIFFERENCE in V ("Electric potential")
between one capacitor plate and the other
which is the same as the battery's potential difference ("Voltage").
Change refers to some original condition, which is irrelevant here.

In fact, EACH spere is a capacitor.
The Surface Area stores increasing charge, as its potential increases.
The one with bigger Area stores that much more charge at the same V
(because the charges are that much farther apart ... V ~ 1/distance).

 

[bethny10]

SO, here's my interpretation:

V(electric potential) = KQ/d

Sphere 1 = KQ/d
Sphere 2 = K2Q/2d
so they have the same V.

right?