I have 2 charged metal conducting spheres which are identical except for having different charge. Sphere A has a charge of -5 nC and sphere B has a charge of -3 nC. I then bring the spheres together so that they touch each other. Afterwards I move the two spheres apart so that they are no longer touching.
What happens to the charge on the two spheres?
What is the final charge on each sphere?
We have two identical negatively charged conducting spheres which are brought together to touch each other and then taken apart again. We need to explain what happens to the charge on each sphere and what the final charge on each sphere is after they are moved apart.
We know that the charge carriers in conductors are free to move around and that charge on a conductor spreads itself out on the surface of the conductor.
When the two conducting spheres are brought together to touch, it is as though they become one single big conductor and the total charge of the two spheres spreads out across the whole surface of the touching spheres. When the spheres are moved apart again, each one is left with half of the total original charge.
Before the spheres touch, the total charge is: -5 nC + (-3) nC = -8 nC. When they touch they share out the -8 nC across their whole surface. When they are removed from each other, each is left with half of the original charge:
on each sphere.
In the previous example we worked out what happens when two identical conductors are allowed to touch. We noticed that if we take two identically sized conducting spheres on insulating stands and bring them together so that they touch, each sphere will have the same final charge. If the initial charge on the first sphere is
and the initial charge on the second sphere is
, then the final charge on the two spheres after they have been brought into contact is:
Two identical, insulated spheres have different charges. Sphere 1 has a charge of
. Sphere 2 has 60 excess electrons. If the two spheres are brought into contact and then separated, what charge will each have?
We need to determine what will happen to the charge when the spheres touch. They are insulators so we know they will NOT allow charge to move freely. When they touch nothing will happen.
Two identical, metal spheres have different charges. Sphere 1 has a charge of
. Sphere 2 has 60 excess protons. If the two spheres are brought into contact and then separated, what charge will each have? How many electrons or protons does this correspond to?
We need to determine what will happen to the charge when the spheres touch. They are metal spheres so we know they will be conductors. This means that the charge is able to move so when they touch it is possible for the charge on each sphere to change. We know that charge will redistribute evenly across the two spheres because of the forces between the charges. We need to know the charge on each sphere, we have been given one.
This problem is similar to the earlier worked example. This time we have to determine the total charge given a certain number of protons. We know that charge is quantized and that protons carry the base unit of charge and are positive so it is
. The total charge will therefore be:
As the spheres are identical in material, size and shape the charge will redistribute across the two spheres so that it is shared evenly. Each sphere will have half of the total charge:
.
So each sphere is now neutral.
No net charge means that there is no excess of electrons or protons.
