Electric Field Distribution in a Charged Hollow Metal Sphere

[Numbnut247]

Hey guys, how do I draw electric fields for this?

A hollow metal sphere with a + charge

http://img340.imageshack.us/img340/9207/untitled2oe.png

Can the electric field be outside of the metal sphere or does it have to be only in the sphere?

 

[berkeman]

Those charges had to come from somewhere. Remember that electric field lines originate on + charges and terminate on - charges (by convention). So the E field for the + charged sphere will start on the surface of the sphere and terminate on the - charges that aren't shown in your diagram. Where do you suppose they are?

 

[Numbnut247]

Would it be one of those:
http://img450.imageshack.us/img450/8461/untitled5ib1.png

What I am confused about are:

1. Are there only 4 electric field lines (cause there are only 4 charges) (I think there are more than 4 lines, but I am not 100 percent sure)

2. Are there electric field lines inside the sphere too? If so how do you draw them? Like mine?

Thanks

 

[RadiationX]

Hey guys, how do I draw electric fields for this?

A hollow metal sphere with a + charge

http://img177.imageshack.us/img177/9522/untitled3qx.png

Can the electric field be outside of the metal sphere or does it have to be only in the sphere?

You have to make the distinction between two types of charge- point charges and charged sphere.

If they are point charges then you are correct. If they are not then the drawing is not correct.

 

[Universe_Man]

hmm.. just learned that this year, I remember too


http://img34.imagevenue.com/aAfkjfp01fo1i-16722/loc177/35605_Field_Lines.JPG

Well, that's how my teacher taught me

 

[berkeman]

Holy cow, do you guys Yahoo? We were just talking about you and your threads over at the Yahoo Physics forums... Yeah, there are 4 point charges on the charged sphere, so your answer is correct.

Over here at the *real* Physics forums, we use actual math to figure stuff out. There's an old dead guy's "law" that you would normally use to figure out this homework question. Hint -- the old dead guy's last name started with a "G".

And if that's not enough (in conjunction with your textbook), here's a link for some reading:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html

 

[mukundpa]

...A hollow metal sphere with a + charge...

Is it possible to have point charges on a metel sphere?

 

[berkeman]

Is it possible to have point charges on a metel sphere?

You charge up a metal sphere by adding excess electrons, or in the case of this problem taking them away to leave a net + charge. For ease in explaining, let me address the case where you add electrons to get a net - charge on the sphere. I suppose you could add a single excess electron, but that's not going to give you much of a charge buildup or electric field. You could add just 2 excess electrons (again not much of a charge), and if you did, they would repel each other and try to end up as far away from each other as possible, so they would end up on opposite sides of the sphere. If there were 4 excess electrons, they would again try to stay as far away from each other as possible.

More practically, you add lots of electrons (or take lots away), and they repel each other enough that they form a uniform distribution of charge around the sphere. The metal sphere forms an "equipotential surface", which means that the whole surface of the sphere is at the same voltage. The source of the electrons that were deposited on the sphere now has fewer electrons than it needs to remain electrically neutral, so it has a net positive charge. You need to know where the electrons came from in order to draw the E field lines that terminate on the sphere in your problem. If the source was another sphere a few radia away to one side, then the E field pattern will be a distribution between the two spheres. If the source of the electrons is a larger concentric sphere that surrounds the first sphere, then the E field lines will be straight radii between the outer sphere and the inner sphere.

And to your question about E field inside the sphere... Remember that E field lines need to originate on + charges and terminate on - charges. Inside the sphere in this problem, you are surrounded by a uniform + charge, and there are no excess - charges anywhere handy.

BTW, this should all be covered in your textbook. Which text are you using? Is this first year college work?

 

[Numbnut247]

You charge up a metal sphere by adding excess electrons, or in the case of this problem taking them away to leave a net + charge. For ease in explaining, let me address the case where you add electrons to get a net - charge on the sphere. I suppose you could add a single excess electron, but that's not going to give you much of a charge buildup or electric field. You could add just 2 excess electrons (again not much of a charge), and if you did, they would repel each other and try to end up as far away from each other as possible, so they would end up on opposite sides of the sphere. If there were 4 excess electrons, they would again try to stay as far away from each other as possible.

More practically, you add lots of electrons (or take lots away), and they repel each other enough that they form a uniform distribution of charge around the sphere. The metal sphere forms an "equipotential surface", which means that the whole surface of the sphere is at the same voltage. The source of the electrons that were deposited on the sphere now has fewer electrons than it needs to remain electrically neutral, so it has a net positive charge. You need to know where the electrons came from in order to draw the E field lines that terminate on the sphere in your problem. If the source was another sphere a few radia away to one side, then the E field pattern will be a distribution between the two spheres. If the source of the electrons is a larger concentric sphere that surrounds the first sphere, then the E field lines will be straight radii between the outer sphere and the inner sphere.

And to your question about E field inside the sphere... Remember that E field lines need to originate on + charges and terminate on - charges. Inside the sphere in this problem, you are surrounded by a uniform + charge, and there are no excess - charges anywhere handy.

BTW, this should all be covered in your textbook. Which text are you using? Is this first year college work?

I'm taking Physics 12 in BC, Canada.

So would this be correct?

http://img58.imageshack.us/img58/1827/untitled5ja.png

 

[Doc Al]

Can you state the exact problem you are trying to solve? Is this a charged metal sphere? What do those four giant + signs represent?

If, as I suspect, this is just a positively charged metal (that is, conducting) sphere, where would the charges be located?

 

[Numbnut247]

Can you state the exact problem you are trying to solve? Is this a charged metal sphere? What do those four giant + signs represent?

If, as I suspect, this is just a positively charged metal (that is, conducting) sphere, where would the charges be located?

This is all I know about the questions:

Draw electric fields for the following:

A hollow metal sphere with a + charge

http://img340.imageshack.us/img340/9207/untitled2oe.png

 

[Doc Al]

OK. Then the diagram you made with the field radiating outward from the surface of the sphere is correct.

To improve your understanding, answer these questions:
(1) Where is the positive charge located? (For example: Is there a positive charge inside the metal? On the inner surface? The outer surface?)
(2) What's the field inside the sphere? (Inside the hollow part? Inside the metal itself?)

 

[Numbnut247]

OK. Then the diagram you made with the field radiating outward from the surface of the sphere is correct.

To improve your understanding, answer these questions:
(1) Where is the positive charge located? (For example: Is there a positive charge inside the metal? On the inner surface? The outer surface?)
(2) What's the field inside the sphere? (Inside the hollow part? Inside the metal itself?)

Thank you. Now the only thing I am still confused about is if I draw only 4 electric field lines (1 for each + charge)?

 

[Doc Al]

Now the only thing I am still confused about is if I draw only 4 electric field lines (1 for each + charge)?

Your 4 + charges is just a fantasy--get rid of them. What you have is metal sphere with an unspecified positive charge. That positive charge represents gazillions of missing electrons on the surface of the sphere, not just 4 positive charges. The positive charge is spread uniformly over the surface of the sphere.

Furthermore, drawing electric field lines as if they were distributed "1 line per 1 charge" is also a fantasy. The lines are just a way to visualize the direction and strength of the electric field; how many you draw is arbitrary. The electric field is what is real, not the field "lines".

 

[Numbnut247]

Kinda off-topic (I didn't want to make a new thread), but do you guys know what happens when a -10uC charged sphere touches a +6uC charged sphere? Would the two spheres turn to -8uC and + 4uC.

u = micro

The original question:

Two small identical spheres contain excess charges of -10uC and +6uC, respectively. The spheres are mounted on insulated stands and placed 0.40m apart.

The spheres are touched together and then returned to their original postion (0.40m apart). Determine the magnitude and direction of the force between the spheres.

I know how to find the force between the spheres (F = kQ1Q2/r^2)but I do not know what the charges are.

 

[Doc Al]

...do you guys know what happens when a -10uC charged sphere touches a +6uC charged sphere?

Here's a hint: The spheres are identical and the charges are free to redistribute themselves (but the total charge remains the same).

 

[Numbnut247]

Here's a hint: The spheres are identical and the charges are free to redistribute themselves (but the total charge remains the same).

I'm thinking that the -10uC sphere's charge will cancel out the other sphere's charge of +6uC. So you will have a -4uC sphere and a neutral sphere. Because they touched, -2uC charge will travel to the neutral sphere. In the end, both spheres will have -2uC as their charges; as a result, when they are separated, the force will be repulsive. Am I right?

 

[Doc Al]

Right. The net charge of -4uC will distribute itself uniformly across both spheres, giving each a charge of -2uC. They will repel each other.

 

[Numbnut247]

Right. The net charge of -4uC will distribute itself uniformly across both spheres, giving each a charge of -2uC. They will repel each other.

Sweet Thanks for all your help