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Homework Help: Gauss' Law & 2 Charged Cylinders

  1. Apr 24, 2005 #1
    Hi, could someone offer some advice on the following problem:

    Q. Using Gauss' law, obtain expressions for the electric field and potential in the space between two thin, hollow, concentric conducting cylinders, of radii a and b, with the outer cylinder connected to earth

    I know that the E-field of the inner cylinder is E=Q/4piEoa^2 in the radial direction (if the cylinder has a charge of Q).

    I also realise that if the outer cylinder was not connected to earth, it's just a capacitor.

    However, I'm really confused as to what affect the earthing of the outer cylinder has on the electric field and potential in between the two cylinders!

  2. jcsd
  3. Apr 24, 2005 #2


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    Suprisingly none. When you use Gauss's law to find the field between the cylinders, you make no reference to the charge outside the gaussian surface. Of course, this is only valid if whatever is out there is cylindrically symmetrical. The only thing that grounding the outer plate does is that it is at potential 0. What does this mean about the field outside the outer cylinder (if it is at the same potential as infinity)? This can tell you what charge has been induced on the outer cylinder.
  4. Apr 24, 2005 #3
    So the external cylinder produces no electric field outside and thus must have the opposite potential to the inner cylinder?
  5. Apr 24, 2005 #4


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    It produces an electric field that puts it at zero potential, which means it is at the same potential as infinity. Basically what you said, switching the words "potential" and "field."
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