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Electric Field Lines sketch

  1. Feb 12, 2007 #1
    1. The problem statement, all variables and given/known data
    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.


    3. The attempt at a solution

    a) [​IMG]

    No electric field lines inside both objects.

    b)[​IMG]

    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.
     
  2. jcsd
  3. Feb 12, 2007 #2

    ranger

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    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.
     
  4. Feb 12, 2007 #3
    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.

    [​IMG]

    3d: [​IMG]
    (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. =/
     
  5. Feb 12, 2007 #4
    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?

    [​IMG]
     
  6. Feb 12, 2007 #5

    ranger

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    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?
     
    Last edited: Feb 12, 2007
  7. Feb 12, 2007 #6
    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 =/
     
  8. Feb 12, 2007 #7

    ranger

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    OK. Lets 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?
     
  9. Feb 12, 2007 #8
    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.
     
  10. Feb 12, 2007 #9

    ranger

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    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 whats 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
     
  11. Feb 12, 2007 #10
    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. =]
     
  12. Feb 12, 2007 #11

    ranger

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    Yup, thats the right picture.
    They will become more concentrated as we get towards the top. And other charges do push them up. But thats 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 wont affect each other. If we keep adding charges to both sides, the charges on one side wont 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?

    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.
     
  13. Feb 12, 2007 #12
    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? [​IMG]

    How would I draw the 3 charges on the tip? Should I just draw them bunched together on the corner?
     
  14. Feb 12, 2007 #13

    ranger

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    Thats the basic idea.
    [​IMG]
    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?
     
    Last edited: Feb 12, 2007
  15. Feb 12, 2007 #14
    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! :smile:
     
  16. Feb 12, 2007 #15

    ranger

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    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!
     
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