# Connecting Charged spheres by a conducting wire

When charged spheres are connected using a conducting wire, the charge will redistribute so as to make the potential constant because the connection makes them a single conductor and conductors are equipotential surfaces.

My doubt was that if the spheres are of different size and have different charges upon them, say q1 and q2 (q2>q1). So after connectiong won't the charges on the two spheres become same? Or will this happen only when the spheres are of same size? Wouldn't this happen for both cases, i.e when both are of same size or different sizes? Just like if an object is hotter than some other object, heat flows out of the hotter object to the less hotter object till both the objects are at the same temperature. So isn't the same analogy applicable here? Excess of charge over one body, so charge flows from the excess body to the other till both have the same charge? Reply soon please!

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## Answers and Replies

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As you say, the charges will distribute themselves so that the common surfaces will be equipotential. Now if the surfaces are very different in shape or size - can the distribution of the charge be uniform?

No it won't be. But does that mean that even after connecting the two bodies, though they have become equipotential but they still are not similarly charged. Can this happen? After connecting if their charge distribution is different, then it means that though they are equipotential there charge distribution is different. This means that some has excess positive charge and the other has less positive charge or has more negative charge. So the more negative charge has a tendency to go towards the excess positive charge to neutralise it. So won't the two sphere be similarly charged after this happens?

ehild
Homework Helper
When charged spheres are connected using a conducting wire, the charge will redistribute so as to make the potential constant because the connection makes them a single conductor and conductors are equipotential surfaces.

My doubt was that if the spheres are of different size and have different charges upon them, say q1 and q2 (q2>q1). So after connectiong won't the charges on the two spheres become same? Or will this happen only when the spheres are of same size? Wouldn't this happen for both cases, i.e when both are of same size or different sizes? Just like if an object is hotter than some other object, heat flows out of the hotter object to the less hotter object till both the objects are at the same temperature. So isn't the same analogy applicable here? Excess of charge over one body, so charge flows from the excess body to the other till both have the same charge? Reply soon please!
When an object is hotter than the other, heat flows out of the hotter one into the other till the temperatures equalize. The same with the charged spheres: charge flows from the one at higher potential to the other, till the potentials become equal. If there is water at different hight in two vessels and you connect them with a tube, water will flow from one to other till the water levels become equal. You can not say that temperature flows from one body to the other or potential flows.

The charge flows from one sphere to the other till the potential of the spheres (with respect to infinity) become equal. You know how the potential is related on the charge and the radius of a sphere. And you know that the whole charge stay the same during the process. From these, you can determine the final charge on the spheres.

ehild

When an object is hotter than the other, heat flows out of the hotter one into the other till the temperatures equalize. The same with the charged spheres: charge flows from the one at higher potential to the other, till the potentials become equal. If there is water at different hight in two vessels and you connect them with a tube, water will flow from one to other till the water levels become equal. You can not say that temperature flows from one body to the other or potential flows.

The charge flows from one sphere to the other till the potential of the spheres (with respect to infinity) become equal. You know how the potential is related on the charge and the radius of a sphere. And you know that the whole charge stay the same during the process. From these, you can determine the final charge on the spheres. As in, no exception has been found to wrong the "flow of charges till surfaces become equipotential" statement?

ehild
Doesn't charge flow until charges become equal? Or as you r saying they flow until potentials become equal. How are we sure about the latter and not about the first? Has this been found out experimentally or something else?

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ehild
Homework Helper
No it won't be. But does that mean that even after connecting the two bodies, though they have become equipotential but they still are not similarly charged. Can this happen? After connecting if their charge distribution is different, then it means that though they are equipotential there charge distribution is different. This means that some has excess positive charge and the other has less positive charge or has more negative charge. So the more negative charge has a tendency to go towards the excess positive charge to neutralise it. So won't the two sphere be similarly charged after this happens?
Less excessive positive charge does not mean more excessive negative charge. If the excess charge was positive, both spheres are positively charged at the end of the process. The sum of the charge on the spheres remains constant. They are not neutralized.

If the potential is the same on both spheres, there is no potential difference to drive charges from one to the other. The electrons do not "know" that they are more on one spheres or the other, and do not "want to go" over. Imagine that there are 20 people in a big room of 40 m2 and there are 6 people in the other room of 6 m2. Do you think that anybody from the bigger room would feel comfortable if he went over to the small room just because there are less people there?

ehild

ehild
Homework Helper
It is an universal law that the intensive parameters tends to equalize in a process that allows the transfer of a quantity. That law was derived from observation.

The driving force for a excessive quantity is the difference of an other "intensive" parameter .
Excessive means a quantity that can be added. Mass is excessive, the total mass of two objects of masses m1 and m2 is m(total)=m1+m2. The total charge of two objects is equal to the sum of the charges on each. The intensive parameters do not add. If a body is at 20 degrees and the other is at 100 degrees, the two will not be at 120 degrees. Allowing thermal contact between them, heat will flow from one to the other, till the temperatures equalize, the bodies are in equilibrium. The hotter cools down, the colder warms up. The final, equilibrium temperature will be between 20 degrees and 100 degrees.

ehild

So the more negative charge has a tendency to go towards the excess positive charge to neutralise it.
You are ignoring that the quantity of charge is only one variable in Coulomb's law. The other variable is distance. Distance is ultimately related to the shape of the system of charges. You cannot single out the charge and dismiss the distance when you consider the distribution of charges in a conductor. The influence of a lot of charge far out can be completely offset by a smallish charge in very close vicinity.