#### Physicsmaster

Well, i recently gave my O-Level Physics (5054) exam, and i found one of the MCQ's about electrostatics pretty tricky, and it got me thinking.

I would like to share it, and i really want to see what others think about this. I asked my teacher, but he can't come up with an explanation!

So, basically.. the MCQ question goes like this:

Which of the following diagrams shows two charged spheres and the force acting on them? [They are asking which diagram shows the correct representation of charge and force].

Option A and D were completely illogical, and showed two like charges attracting, and two opposite charged spheres repelling. So ofcourse, they are wrong.
They were:

But then came the problem; Option B and C.
They both show the correct force, but the problem is the charge distribution.
Is there even supposed to be charge distribution in two charged spheres when attracting or repelling?

Here are Option B and C:

I chose C, the one with the attraction. How do we make the right choice?

In some of the spheres, the charge was on the right, but in some it was on the left. Why? Shouldn't the charge be spread uniformly? Or does the charge distribution change during attraction and repulsion?

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#### Physicsmaster

Ugh.

When we charge a sphere positive, all the free-electrons have been removed. Yes or No? That means there are no electrons in it, that can be repelled.

There exists only negative charge that can move. Only electrons can move. A place with excess of electrons has negative charge. And a place on the sphere that has lack of electrons is positively charged. The protons don't move. They are in the atoms. It is the absence and presence of electrons that determines the charge. The Sphere that has excess electrons due to charging, then it has an overall negative charge.
A sphere that is positively charged, it has a lack of electrons, as they have been removed by charging method, to the earth.

Now, if we bring the positively charged sphere near the negatively charged one, is the charge distribution supposed to change? is the negative charge supposed to be repelled to the end or something?

When two positively charged spheres are brought near to each other (Option B), are the positive charges supposed to be repelled away to the edges?

Positive charges don't move! Only electrons can move. If the positive charge is shown on the edges, that means the electrons have moved towards the other edge on both spheres. Firstly, there should be no free electrons, since it's positively charged. Right?

Even if they were there, why would they move inwards, shouldn't the electrons on one sphere repel the electrons in the other sphere? Why would the positive charges go to the edges during repulsion?

Or is this question completely illogical? I DON'T GET IT!

Are charges pushed to the edges during repulsion?

I mean, if the two spheres were negatively charged with an excess of electrons, i can imagine the electrons being pushed outwards on both spheres, and negative charge at the edges of both spheres, outwards. But in the case of two positive charged spheres, i don't think the positive charge should be at the edges!

#### Physicsmaster

Come on. Please say something. If you don't understand something, ask.. I will clarify!

#### Physicsmaster

.

If two negatively charged metal spheres were brought close to each other, negative charges would be spread to their outer edges, because electrons on one sphere repel the electrons on the other sphere.

This will happen, i guess. And then the two negatively charged spheres will repel. Note the electrons can move, that is why the negative charge went to the edges.

But what about two positively charged spheres? Will it be like in Option B? Will the positive charge be repelled to edges? I don't think so.
In the case of negative charged metal spheres, electrons can move, so they moved to the edges. But in positively charges spheres, positive charge can't move. As i said, it is simply the absence of electrons. So if the question says the positive charges moved to edges, that means electrons moved inwards, and why would they move inwards? So No. I think it's wrong! So am i right? :'(

#### topsquark

Forum Staff
But then came the problem; Option B and C.
They both show the correct force, but the problem is the charge distribution.
Is there even supposed to be charge distribution in two charged spheres when attracting or repelling?

Here are Option B and C:

I chose C, the one with the attraction. How do we make the right choice?

In some of the spheres, the charge was on the right, but in some it was on the left. Why? Shouldn't the charge be spread uniformly? Or does the charge distribution change during attraction and repulsion?
We would need more information. If I had to hazard a guess (I'm doing that a lot today!) are the spheres conductors? In that case opposing charges would attract and they would accumulate on the facing sides of the spheres. For like charges they would repel and be on opposite sides of the spheres. So for a conductor I would say that B is correct.

If they are not conductors it would likely depend on how they are charged and the specific nature of the dielectric, but I would say both choices might be possible.

And hey! We'll get to your question. Don't be so impatient!

-Dan

#### topsquark

Forum Staff
When we charge a sphere positive, all the free-electrons have been removed. Yes or No? That means there are no electrons in it, that can be repelled.

There exists only negative charge that can move. Only electrons can move. A place with excess of electrons has negative charge. And a place on the sphere that has lack of electrons is positively charged. The protons don't move. They are in the atoms. It is the absence and presence of electrons that determines the charge. The Sphere that has excess electrons due to charging, then it has an overall negative charge.
A sphere that is positively charged, it has a lack of electrons, as they have been removed by charging method, to the earth.

Now, if we bring the positively charged sphere near the negatively charged one, is the charge distribution supposed to change? is the negative charge supposed to be repelled to the end or something?

When two positively charged spheres are brought near to each other (Option B), are the positive charges supposed to be repelled away to the edges?

Positive charges don't move! Only electrons can move. If the positive charge is shown on the edges, that means the electrons have moved towards the other edge on both spheres. Firstly, there should be no free electrons, since it's positively charged. Right?

Even if they were there, why would they move inwards, shouldn't the electrons on one sphere repel the electrons in the other sphere? Why would the positive charges go to the edges during repulsion?

Or is this question completely illogical? I DON'T GET IT!

Are charges pushed to the edges during repulsion?

I mean, if the two spheres were negatively charged with an excess of electrons, i can imagine the electrons being pushed outwards on both spheres, and negative charge at the edges of both spheres, outwards. But in the case of two positive charged spheres, i don't think the positive charge should be at the edges!
I think the biggest difficulty you are having is that a positively charged (conducting again?) sphere has no free electrons. Free electrons in a metal are actually "smeared out" across the volume of the conductor. An object is negatively charged only when it has more electrons than the number of protons in the object. Likewise an object is positively charged when there are fewer electrons than the number of protons. But there will be plenty of free electrons left over in either case.

You are correct...the positive charges do not move. But if we move electrons (or other motile negative charges) from a region it will have an overall positive charge. So if you have a current of electrons moving from one place to another you can also view this as "positive charges" moving in the opposite direction. It's just easier to think of it in terms of positive charges. (If you continue in Physics you will learn about "holes." Holes occur in atomic states when an electron is missing. They have no real existence but they act just like an electron, but with a positive charge. They even have an effective mass which is the same as an electron's. But do not confuse them with the anti-particle of the electron: the positron. Positrons are real (anti)particles...holes are not real particles, just a useful concept.)

-Dan

#### Physicsmaster

..

They are charged METAL spheres. I forgot to mention METAL, so yes, they are conductors. Now, you pointed out that when two oppositely charged metal spheres attract, the positive and negative charges come to the facing sides of the spheres. And for two like charged spheres the charges move to the non-facing sides of the spheres followed by the repulsive force.

But my entire point is based on the fact that positive charge can not move. The metal sphere has metallic bonding, consisting of positively charged metal ions immersed in a sea of free electrons. When we charge a metallic sphere positive, we are actually removing the free electrons (All of them? Or some of them? I am still not clear about this. I think all of the free electrons are removed).

So, if two negatively charged spheres are brought close to each other, i understand the concept that the electrons in one would repel the electrons in the other one, and the negative charges would be distributed on the non-facing sides like this, followed by a repulsive force.

But what about two positively charged sphere?
The positive charge would certainly not be repelled to the non-facing sides. The Positive charge CAN-NOT move. It is the electrons that move, and the electron-excess areas are negatively charged, and the electron deficient areas are positively charged.

So, let's assume that the positive charges moved to the non-facing sides, before repulsion. That would mean the free electrons (which i am still not sure are present after charging, in a positively charged metal sphere?) moved in the opposite direction to the facing side of the two spheres. So the electrons in both spheres are moving towards the facing sides. Shouldn't the two negative charges and electrons repel?

#### Physicsmaster

..

Basically.

These are my queries:

1. I understand that metals have metallic bonding, in which there are metal positive ions, and the valence electrons have been removed and form the sea of delocalized electrons that hold the metallic lattice together. But the other electrons, are still in the inner shells. It's only the outer-shell electrons that have been removed to form a metallic structure. Now, during charging of a metal sphere, these free electrons are repelled to the other side, by a negatively charged rod, and then that side is earthed, leading to all those free electrons travelling to the earth and the negative charge on the earthed side being neutralized. And then the earthing is removed, and the negatively charged rod is removed. We get a positively charged metal sphere. Now my question is. Are all the free electrons removed? The negatively charged rod pushed all the free-moving electrons towards the other side that was earthed. So technically, i believe that all the free electrons have been removed from the metallic sphere. Am i right? Now, the positively charged metal sphere has no free electrons.

2. Okay. So i know the concept of electrostatic induction. When a charged object is brought close to an uncharged one, the charges are SEPARATED. But then the uncharged object is attracted to the charged object due to force of attraction with the opposite charge on the facing side, which is greater than the force of repulsion with the charge induced on the opposite side.

Now i had the concept that distribution and separation of charge only occurs in such a situation. But now they give a question where two CHARGED metal spheres are placed close to each other. I understand that like charged metal spheres should repel, and unlike should attract. But the concept of the charges being pushed to the sides and towards the facing sides is something i do not understand. Why are the charges being pushed away or moved towards the facing side? If we have a positively charged sphere, it is UNIFORMLY positive. It has no free-electrons, or only some. But if it is brought near to another positively charged sphere, how can we say that the positive charges would be pushed to the non-facing sides? Positive charge CAN NOT move. So the electrons must have moved in the opposite directions. And the electrons, i am not even sure are present, or only a few are present. So they must have moved towards the facing side. Why would the electrons of both spheres, move towards the facing side? Electrons should repel electrons. Why are the electrons travelling towards the facing side, leading to positive charge being placed on the non-facing sides, BEFORE REPULSION?

3. Is there any way i can prove this question. The one i have been given in my exam, to be wrong? Can i point out any mistake? Maybe that the movement of positive charges to the non-facing sides is not possible?

4. You said that when two oppositely charged spheres are brought close to each other, their opposite charges come towards the facing side. But again, we know for a fact that only ELECTRONS move. That means the electrons of one sphere moved [For what reason?] to the facing side, and repelled the electrons of the other sphere away, causing a positive charge on the side of the positive sphere facing the negative one. The sphere was already positive. But the point is, the positive charge concentration was shifted towards the facing side, due to the two oppositely charged spheres being placed close to each other. Can't this entire attraction force happen without the charges coming towards the facing side? Can't the negative charge be uniformly distributed on one sphere, and the positive on one sphere, and they attract one another as unlike charges attract. Why are the charges moving to the facing side?

I am really confused! There is so much about physics that i don't know.

For some people it might be as simple, as just saying that opposite charges come close on the facing sides and attraction happens. But i can't believe this until i go in depth into this matter.

#### topsquark

Forum Staff
Basically.

These are my queries:

1. I understand that metals have metallic bonding, in which there are metal positive ions, and the valence electrons have been removed and form the sea of delocalized electrons that hold the metallic lattice together. But the other electrons, are still in the inner shells. It's only the outer-shell electrons that have been removed to form a metallic structure. Now, during charging of a metal sphere, these free electrons are repelled to the other side, by a negatively charged rod, and then that side is earthed, leading to all those free electrons travelling to the earth and the negative charge on the earthed side being neutralized. And then the earthing is removed, and the negatively charged rod is removed. We get a positively charged metal sphere. Now my question is. Are all the free electrons removed? The negatively charged rod pushed all the free-moving electrons towards the other side that was earthed. So technically, i believe that all the free electrons have been removed from the metallic sphere. Am i right? Now, the positively charged metal sphere has no free electrons.

2. Okay. So i know the concept of electrostatic induction. When a charged object is brought close to an uncharged one, the charges are SEPARATED. But then the uncharged object is attracted to the charged object due to force of attraction with the opposite charge on the facing side, which is greater than the force of repulsion with the charge induced on the opposite side.

Now i had the concept that distribution and separation of charge only occurs in such a situation. But now they give a question where two CHARGED metal spheres are placed close to each other. I understand that like charged metal spheres should repel, and unlike should attract. But the concept of the charges being pushed to the sides and towards the facing sides is something i do not understand. Why are the charges being pushed away or moved towards the facing side? If we have a positively charged sphere, it is UNIFORMLY positive. It has no free-electrons, or only some. But if it is brought near to another positively charged sphere, how can we say that the positive charges would be pushed to the non-facing sides? Positive charge CAN NOT move. So the electrons must have moved in the opposite directions. And the electrons, i am not even sure are present, or only a few are present. So they must have moved towards the facing side. Why would the electrons of both spheres, move towards the facing side? Electrons should repel electrons. Why are the electrons travelling towards the facing side, leading to positive charge being placed on the non-facing sides, BEFORE REPULSION?

3. Is there any way i can prove this question. The one i have been given in my exam, to be wrong? Can i point out any mistake? Maybe that the movement of positive charges to the non-facing sides is not possible?

4. You said that when two oppositely charged spheres are brought close to each other, their opposite charges come towards the facing side. But again, we know for a fact that only ELECTRONS move. That means the electrons of one sphere moved [For what reason?] to the facing side, and repelled the electrons of the other sphere away, causing a positive charge on the side of the positive sphere facing the negative one. The sphere was already positive. But the point is, the positive charge concentration was shifted towards the facing side, due to the two oppositely charged spheres being placed close to each other. Can't this entire attraction force happen without the charges coming towards the facing side? Can't the negative charge be uniformly distributed on one sphere, and the positive on one sphere, and they attract one another as unlike charges attract. Why are the charges moving to the facing side?

I am really confused! There is so much about physics that i don't know.

For some people it might be as simple, as just saying that opposite charges come close on the facing sides and attraction happens. But i can't believe this until i go in depth into this matter.
Okay, think of the free electron problem this way. The metal is bonded because these electrons are present. Think of it as all the free electrons are "shared" with all of the atoms in the metal. This is what causes the bonding. If the free electrons were all gone there would no longer be a metallic bond and the metal would fall apart! The induction/grounding method you mentioned gets rid of excess electrons in the system to the ground. Most of the free electrons are still present in the metal.

Also, since we are talking about a metal all of the charge imbalances are on the surface of the metal, not in the interior. (You don't actually need to know that, but it's true.) If we have a charged negative sphere and bring it close to another the charges in each are free to move around. As negative charges repel they will tend to try to get as far away from each other as possible. But don't think that all the negative charges go to the opposite side...the electrons in a single sphere still want to avoid each other so they can't all just accumulate on one side. A balance is obtained where there is a larger negative charge on opposing sides of the sphere. The actual charge distribution can get rather complicated so they teach you that it all goes to one side.

We can make a similar argument in the positive charge scenario. Say we have two positively charged metal spheres coming close to each other. The atomic sites can't move, but the electrons still can. And electrons want to get close to positive charges. So what happens is that the electrons in the sphere on the right want to crowd in closer to the sphere on the left. And that means that there ends up being fewer electrons on the far sides of the spheres, meaning there is a net positive charge on the far sides of the spheres. You can always explain these things by movement of electrons but most people find it simpler to talk about "positive charges moving." It's inaccurate, but easier to understand how to manipulate the situations.

You had four questions, but I think this covers all the topics. Let me know if you are still confused.

-Dan

#### Physicsmaster

..

I still don't get why in the positively charged sphere situation, when two positively charged metal spheres are brought near each other, why the electrons move inwards, towards the facing sides. .-.
That is completely pointless. The repulsion should be a result of positively charges on one spheres repelling the positive charges of the other. No point in electrons moving inwards, as they are like charged, and they should try to move away, not towards each other.

Also, you mentioned that the ''excess' electrons in the metal are removed during charging. The thing is, there are no excess electrons in a NEUTRAL metallic sphere. That is what makes it neutral. The number of electrons, including the ones that are free (the outer-shell ones), and the ones in the shells, are equal in number to the number of protons in all the nuclei. This is what makes the metallic body neutral. But once it is charged, it must be the free-electrons that are free to move, that are removed. Resulting in lesser number of electrons as compared to protons, leading to an overall positive charge on the metal sphere.