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Electric Field inside concentric spherical shells

  1. Feb 3, 2015 #1
    1. The problem statement, all variables and given/known data

    I uploaded a file that gives the problem statement.

    2. Relevant equations

    I don't believe any equations are necessary. However, I could be wrong. I believe it to be a concept question. The relevant concept being that the electric field inside conducting materials in equilibrium is equal to zero.


    3. The attempt at a solution

    I am not feeling super confident but here is my attempt:

    A, C,D,E,F all zero. and B = -1uC

    If I am way off base just say so and I will give the problem a few more brain cycles. If there is a relevant equation that I am missing please let me know.
     

    Attached Files:

  2. jcsd
  3. Feb 3, 2015 #2

    haruspex

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    That is within the body of the conducting material. Inside a hollow within the body there may be a field if there are other charged bodies within the hollow.
     
  4. Feb 3, 2015 #3
    I see, okay well can you give me a hint about what the distance has to do with anything? The only equation I could come up with was EA = Q(enclosed)/E(knot) which does not involve distance. I guess what I am trying to ask is:

    At point F, can I say that E = (16uC)/(E(knot)4pi(12d)^2)?
     
    Last edited: Feb 3, 2015
  5. Feb 3, 2015 #4

    haruspex

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    Each shell will have an induced charge distribution. Describe it in broad terms.
    Next, consider point B. What field results at point B from those charge distributions?
    What about point C, etc?
     
  6. Feb 3, 2015 #5
    I am not sure what you mean by an induced charge distribution. I didn't get this part when my professor tried explaining it in class either. Should I assume that the net charge for the all the shells is 19-4+1 = 16uC?
     
  7. Feb 3, 2015 #6

    haruspex

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    Yes, that's the net charge of the system.
    Because each shell is a conductor, the charges on it will be distributed on the surfaces. I.e. a charge distribution on the inside of each shell and another on the outside of each shell.
    By the symmetry of the set-up, each of these six charge distributions will be uniform.
    The total charge on each shell is given, so there are in effect three unknowns. The charges on each shell will arrange themselves so that there is no net field (after taking into account all the other shells) within its conducting material.
    In the special case of a hollow conductor with no charged objects in the hollow, there is no field in the hollow either.
    So, considering potentials, there is a uniform potential within the central hollow and continuing through the innermost shell to its outer surface. There may be a potential gradient (hence a field) from there to the inner surface of the next shell, then no further change in potential until its outer surface, and so on.

    One way to attack this problem is to assign a symbolic variable to each of the six charges (or to the charge densities if you prefer). You have immediately the three equations for the total charge on each shell.
    Next, you can calculate the potential at any given point in the system in terms of those six charges. (To do this you have to know the standard formulae for potential inside and outside uniformly charged spherical shells. These are essential knowledge for the subject. They should have been quoted in the OP as relevant equations.)
    You can now write down three more equations corresponding to the fact that for each shell the potential is the same at its inner surface and its outer surface.
    Six equations, six unknowns. Solve.

    That gives you all the charge distributions. At any given point, you can compute the field due to each charge distribution and add them (vectorially)... or you can find the expression for the potential in a small neighbourhood of the point and differentiate to find the field.
     
  8. Feb 3, 2015 #7
    Ah I see okay well I guess there is still one part I find confusing. For the point D, should I assume the charge on that shell lies beyond the point D on the outside of it? I mean say I had a point charge inside one shell. The point charge q = 2c and the shell q = -2c. Now lets say I want E for a point that lies inside of the shell at some distance r (like D). Can I say that would just be = kq/r^2? Or, do I have to take the shell's charge into account somehow?
     
  9. Feb 3, 2015 #8

    haruspex

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    As I wrote, you should assume a charge on each surface of each shell (since the shells have significant thickness). Six thin shells of charge in all.
    Can you quote the general formula for the field from a uniformly charged thin shell? (It has two distinct cases.)
     
  10. Feb 3, 2015 #9
    Let me ask a new question that might clear things up for me:

    Lets say a -2q net charge spherical insulator is placed inside a charged spherical conducting shell of net charge +4q. Now, if I say I have a point A which lies on the inside of the shell and a point C on the outside of the shell. I think I can say that point A has a net charge of +2q. However, if I now move to a point C in between A and B here I am lost. Is the net charge here zero? If it is does that make E at the point zero as well?
     
    Last edited: Feb 3, 2015
  11. Feb 4, 2015 #10

    haruspex

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    No, you can't talk about a charge at a point, except where a point charge exists in the set up. You can discuss the potential at A and the field at A.
    You're asking quite a complicated question, and we need to start with something simpler. Please answer my question in post #8. If there is a thin uniformly charged shell of radius R:
    - what is the field at a distance r < R from the centre of the shell?
    - what is the field at a distance r > R from the centre of the shell?
    These formulae are basic to your given question. Without them, you cannot answer it; with them it's not hard.
    If you don't know, read http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html
     
  12. Feb 4, 2015 #11
    Your right sorry I should have specified that the point A was really the inside of the shell (not the point exactly) but the charge on the inside of the shell. To answer your questions: for r < R, E = 0 for r > R I treat it like a point charge kQ/r^2.
     
  13. Feb 4, 2015 #12
    Is this correct?:

    A) zero
    B) (.5uC*k)/(d/2)^2
    C) (1uC*k)/(3d)^2
    D) (3uC*k)/(5d)^2
    E) (-3uC*k)/(9d)^2
    F) (16uC*k)/(12d)^2
     
    Last edited: Feb 4, 2015
  14. Feb 4, 2015 #13

    haruspex

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    B and D are wrong.
     
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