How Does Grounding Affect Charge Distribution on a Conductor?

[Saitama]

Homework Statement

A positively charged ball is brought close to a neutral isolated conductor. The conductor is then grounded while the ball is kept close. Is the conductor charged positively, negative or neutral, if (a) the ball is first taken away and then the ground connection is removed and (b) the ground connection is first removed and then the ball is taken away?

Homework Equations

The Attempt at a Solution

This may be a very basic question but i am completely new to this subject.
Firstly, i don't understand what happens when the conductor is grounded.
I guess when the positively charged ball is brought closed to the conductor, the electrons attract towards the positively charged ball and accumulate on one side of the conductor. Now the question is what happens when the conductor is grounded?

Any help is appreciated! :)

 

[QuarkCharmer]

Think of the Earth as this big giant pool of positive and negative charges. There are just so many charges in it that taking some, or removing some really doesn't change it at all and so it's neutral. When you "ground" the neutral plate for instance, you are giving it a pipeline to all these charges.

Think about what would happen when the charged ball got near the plate and the plate was grounded. Induction is going to occur, what sort of charge will it induce on the plate?

 

[Saitama]

Think of the Earth as this big giant pool of positive and negative charges. There are just so many charges in it that taking some, or removing some really doesn't change it at all and so it's neutral. When you "ground" the neutral plate for instance, you are giving it a pipeline to all these charges.

There will be no charge flow if a neutral plate is grounded. *unsure*

Think about what would happen when the charged ball got near the plate and the plate was grounded. Induction is going to occur, what sort of charge will it induce on the plate?

Yes, i know that induction will occur but i got stuck when it says "ground" the conductor.
My guess is that there will be a flow of electrons from the Earth to the plate.

 

[QuarkCharmer]

If the positive ball comes near the neutral plate, a charge will be induced. One way or another, negative charges are going to build up on the side of the plate near the ball. If the plate is not grounded it will have to rearrange it's own charge such that it has a net negative charge near the ball, and a net positive somewhere else.

If the plate has a magical pipeline (ground) to unlimited charge, why would it rearrange it's own charge, when it can just suck some up from the pipe and put it near the ball? What happens to the total charge on the plate when the pipeline is removed then?

 

[Saitama]

If the plate has a magical pipeline (ground) to unlimited charge, why would it rearrange it's own charge, when it can just suck some up from the pipe and put it near the ball? What happens to the total charge on the plate when the pipeline is removed then?

If the ball is still kept close to the plate and the pipeline is removed, maybe the charge again gets rearranged but this time there will be negative charge on the other side of plate too where previously positive charge was present when we did not ground the plate.
There will be negative charge on both sides because already negative charge is accumulated on one side (the side where the positively charged ball is present), the coming negative charge will face repulsion and move to the other side.

 

[QuarkCharmer]

Thats the right idea, there really isn't any other "rearranging of charges" going on though.

If the net positive ball is kept near the plate, and the now net negative plate is then ungrounded, it has all this extra negative charge on it that it can't get rid of. The negative charge on the plate is more dense in the area near the ball, since the ball is still inducing a charge. Now, if the ball is removed, the plate has a net negative charge, which is more dense in one region, that will eventually even out over the whole plate given enough time.

If this process is completed, and the net positive ball is removed along with the ground. You have essentially transferred negative charge from the ground to the otherwise neutral plate, making it now net negative.Basically it's this:
Your friend comes up to your window and he's really thirsty. You have just enough water in your fridge for yourself, but you realize that you can get a basically endless supply from the tap. So you get out a bucket and fill it up from the tap. Just when you are done filling, the utilities company cuts off your water and sewage for maintenance. You also can't manage to give the bucket of water to your buddy because the window is locked and your stupid ex-wife got the keys in the divorce! So your friend leaves and now you have more water than you can drink, and you can't even dispose of it.

 

[Saitama]

Thats the right idea, there really isn't any other "rearranging of charges" going on though.

If the net positive ball is kept near the plate, and the now net negative plate is then ungrounded, it has all this extra negative charge on it that it can't get rid of. The negative charge on the plate is more dense in the area near the ball, since the ball is still inducing a charge. Now, if the ball is removed, the plate has a net negative charge, which is more dense in one region, that will eventually even out over the whole plate given enough time.

If this process is completed, and the net positive ball is removed along with the ground. You have essentially transferred negative charge from the ground to the otherwise neutral plate, making it now net negative.

Thank you for the explanation QuarkCharmer!

Getting back to the question, i guess for both the parts, the conductor is negatively charged.

Basically it's this:
Your friend comes up to your window and he's really thirsty. You have just enough water in your fridge for yourself, but you realize that you can get a basically endless supply from the tap. So you get out a bucket and fill it up from the tap. Just when you are done filling, the utilities company cuts off your water and sewage for maintenance. You also can't manage to give the bucket of water to your buddy because the window is locked and your stupid ex-wife got the keys in the divorce! So your friend leaves and now you have more water than you can drink, and you can't even dispose of it.

LOL. I get it. :rofl: :rofl:

 

[QuarkCharmer]

Not exactly.

For the first part, if the ball is taken away, and enough time passes before the ground is removed, the net negative charge in the plate will go back into the ground. The final result will be that the plate has a neutral charge. That's probably what they are looking for, since the flow of electrons is seemingly instantaneous.

In reality though, it depends on the materials and other factors which determine how long it takes for the charge to flow back out. But in these sort of "idealized" problems, it's probably best to think that the charges instantly go back to the Earth when the ball is removed.

 

[Saitama]

Not exactly.

For the first part, if the ball is taken away, and enough time passes before the ground is removed, the net negative charge in the plate will go back into the ground. The final result will be that the plate has a neutral charge. That's probably what they are looking for, since the flow of electrons is seemingly instantaneous.

Thank you for clarifying it. So grounding basically means that if the negative charge is in excess, it flows to the ground and if it is less, the negative charge flows from ground to the plate.
By the way, if it was a positively charged plate and we ground it, will the negative charge from the ground to the plate?

 

[QuarkCharmer]

That's right.