Sketching Electric Field Patterns for Charged Objects

[AznBoi]

Homework Statement

a) Sketch the electric field pattern setup by a postively charged hollow sphere. Include regions inside and regions outside the sphere. b) A conducting cube is given a positive charge. Sketch the electric field pattern both inside and outside the cube.

The Attempt at a Solution

a) http://img250.imageshack.us/img250/7113/hollowspherent3.th.png

No electric field lines inside both objects.

b)http://img111.imageshack.us/img111/8013/conductingcube2dib9.th.png

My teacher said for the cube, the lines radiating outwards: Except they’re more bunched up around the corners.

Can someone explain what that is suppose to mean? Should I draw my pictures in 3d or 2d? Please tell me if I'm doing this right.

 

[ranger]

My teacher said for the cube, the lines radiating outwards: Except they’re more bunched up around the corners.

Now we know that surface is littered with positive charges, which of course [repel] other. The further the charges are from each other, the less concentrated the total charge is for the area, and so is the electric field. But if we take the corner of the cube...do you catch my drift?

Hint: picture the repulsion force parallel to the surface of the cube.

 

[AznBoi]

Now we know that surface is littered with positive charges, which of course [repel] other. The further the charges are from each other, the less concentrated the total charge is for the area, and so is the electric field. But if we take the corner of the cube...do you catch my drift?

Hint: picture the repulsion force parallel to the surface of the cube.

What's different with the corner of the cube? Wouldn't the charges still uniformly spread out around the cube so that the distant between each charge are the same? I know that there are 3 sides that join together to form a cube's corner but I still don't get the visual picture. Is it because I'm drawing only a surface of the cube? or does that not make a difference? Would the charges still be bunched up around the corners in a square drawing?

Here are my revisions, although I'm still not quite understanding this.

http://img127.imageshack.us/img127/8495/conductingcube2dkj6.th.png

3d: http://img294.imageshack.us/img294/3331/conductingcubecl5.th.png
(You can ignore the lines within the cube)

But still, aren't the charges in the 3d drawing still uniformly spread out? I don't get where the bunched up corners come in. =/

 

[AznBoi]

I think the lines should look like this, but I'm still unsure of where the charges go. Are they literally bunched up in the corner? and the ones on the flat sides are uniformally distributed? Why is this?

http://img162.imageshack.us/img162/8448/cubelinesdw8.th.png

 

[ranger]

What's different with the corner of the cube? Wouldn't the charges still uniformly spread out around the cube so that the distant between each charge are the same? I know that there are 3 sides that join together to form a cube's corner but I still don't get the visual picture. Is it because I'm drawing only a surface of the cube? or does that not make a difference? Would the charges still be bunched up around the corners in a square drawing?

Notice I said that the repulsion force is directed parallel along the surface of the cube. Now if the charges are being repelled by other charges, how would you describe the cause of the "bunched" up electric field at the corners? And no, charges are not distributed uniformly across the surface of a cube, if it were then how would you explain the bunched up electric field lines at the corners?

 

[AznBoi]

Notice I said that the repulsion force is directed parallel along the surface of the cube. Now if the charges are being repelled by other charges, how would you describe the cause of the "bunched" up electric field at the corners? And no, charges are not distributed uniformly across the surface of a cube, if it were then how would you explain the bunched up electric field lines at the corners?

Well I visualize as 3 sides, have a charge being pushed into the corner on each of the sides so that there are 3 charges in a cube's corner. Does that mean I have to draw a 3d model, I don't get how the charges can be bunched up in a 2d model. They all repel each other so that the space between each are the same? Confused =/

 

[ranger]

OK. Let's step down from the cubed scenario so that you can get a better understanding for the cause of the charge bunch at the corners. I want you to consider a simple line (flat surface) for which positive charges are distributed about the surface. As I mentioned before, the repulsion force (direction of force) that one charge experiences due to another is parallel to the surface. Are the charges distributed uniformly about the surface? Why?

 

[AznBoi]

OK. Let's step down from the cubed scenario so that you can get a better understanding for the cause of the charge bunch at the corners. I want you to consider a simple line (flat surface) for which positive charges are distributed about the surface. As I mentioned before, the repulsion force (direction of force) that one charge experiences due to another is parallel to the surface. Are the charges distributed uniformly about the surface? Why?

Well shouldn't the charges be distributed evenly if all of the charges have a 360 degree electrical field around them pushing the like charges away? They could form uniform lines, triangles, etc. but the distance between the charges would always be the same correct?

I haven't gone really indepth about electical fields. I just know the basics like the lines must begin on positive charges and end on negatives. The number of lines is proportional to the magnitude of the charge etc.

 

[ranger]

Well shouldn't the charges be distributed evenly if all of the charges have a 360 degree electrical field around them pushing the like charges away? They could form uniform lines, triangles, etc. but the distance between the charges would always be the same correct?

Yup, your thinking is correct. There should be a uniformity. But instead of saying electric field around them, its better to say repulsive force, as this is what's determines the spacing between charges. Scratch that thought about triangles.

Now what happens if we take the flat surface and elevate just a small portion of it, so we have a flat, then a bump, followed by a flat. How will the charges be affected by this? Note that I'll say again, the repulsion force is parallel to the surface. Are the charges still uniform about the surface?
The number of lines is proportional to the magnitude of the charge

 

[AznBoi]

Yup, your thinking is correct. There should be a uniformity. But instead of saying electric field around them, its better to say repulsive force, as this is what's determines the spacing between charges. Scratch that thought about triangles.

Now what happens if we take the flat surface and elevate just a small portion of it, so we have a flat, then a bump, followed by a flat. How will the charges be affected by this? Note that I'll say again, the repulsion force is parallel to the surface. Are the charges still uniform about the surface?
The number of lines is proportional to the magnitude of the charge

If you have surface with a bump in it, it would look like a hill right? I think that the chargers will gather up on the hill because.. I'm not sure the others push them up? And there could be many charges on that hill because it is like a ladder and each charge goes on every step unaffecting the charges above or below because the replusive force is parallel or horizontal to the surface.

Why is the replusive force parallel to the surface and not 360 degrees? Thanks for taking your time to help by the way. =]

 

[ranger]

If you have surface with a bump in it, it would look like a hill right?

Yup, that's the right picture.

I think that the chargers will gather up on the hill because.. I'm not sure the others push them up?

They will become more concentrated as we get towards the top. And other charges do push them up. But that's the key, they are only pushed up becuase no charges in front of them will affect it becuase the forces are parallel along the surface (and weak for an individual charge). Imagine two charges, one on each side of the mountain, becuase the repulsion force is parallel, they won't affect each other. If we keep adding charges to both sides, the charges on one side won't affect the charges on the other. So when the charges on one side is pushed towards the top, there is nothing pushing it down. Of course when you have charges on one side of the mountain, one after the other, they do repel each other, put it is usually a weak force so they continue to accumulate anyway. Do you get my drift?

Why is the replusive force parallel to the surface and not 360 degrees? Thanks for taking your time to help by the way. =]

Actually it is. But when a charge is on a flat surface, we only care about the force that is parallel to the surface, as the charge is 180 degrees with respect to each other.

 

[AznBoi]

Yeah I get it somewhat. If you have charges on one side of the mountain and on the other side, they can't push each other off? O----> <-----O
I'm mostly confused about the direction of the electric forces.

Anyways, I guess the corner of the cube would be like the hill right? More charges would accumulate at the tip rather than on the flat sides.

So would this drawing be right? http://img263.imageshack.us/img263/8012/cubelinesrz0.th.png

How would I draw the 3 charges on the tip? Should I just draw them bunched together on the corner?

 

[ranger]

Yeah I get it somewhat. If you have charges on one side of the mountain and on the other side, they can't push each other off? O----> <-----O

Thats the basic idea.
http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l4d6.gif

Anyways, I guess the corner of the cube would be like the hill right? More charges would accumulate at the tip rather than on the flat sides.

So we can safely conclude that charges will accumulate at places with the greatest curvature.

And about your diagram. Do you really have to show individual charges? Wont it just be enough to show greatest concentration of field lines at the corners?

 

[AznBoi]

Thats the basic idea.
http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l4d6.gif

So we can safely conclude that charges will accumulate at places with the greatest curvature.

And about your diagram. Do you really have to show individual charges? Wont it just be enough to show greatest concentration of field lines at the corners?

Yeah, I guess I won't show the individual charges. I would assume that the charges aren't drawn correctly then? xD Thanks a lot for your help!

 

[ranger]

You're charges are drawn correct, but drawing only field lines, you'll get the point out more about concentrated electric field. If you put the charges in, you'll most likely clutter up the diagram. Leave them in if you wish to though.

You're welcome!