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Parallel plates, calculate charges and E. fields without surface area?

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    two metal plates 10mm thin are held a distance 40mm apart with a P.D. 10V across them. +ve plate on left. In between the plates is a vacuum (free space basically). Calculate the charges and electric fields within this system.


    2. Relevant equations
    Q=VC
    C = εo.A/d
    No surface area given, so how to do it?

    E = V/d can be done but is that what is asked for?

    3. The attempt at a solution
    ????
     
  2. jcsd
  3. Nov 2, 2009 #2

    Delphi51

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    Homework Helper

    E = V/d gives you the electric field between the plates and you can use Gauss' Law to get the charge per unit area on each plate.
     
  4. Nov 3, 2009 #3
    no surface area, bra`

    ok so gauss' law is...
    [tex]\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}[/tex]

    so how do I use that?
     
    Last edited: Nov 3, 2009
  5. Nov 6, 2009 #4
    So you can determine the electric field. Recall for parallel plates that

    [tex] E = \frac{\sigma}{2\epsilon_{0}} [/tex]

    Sigma is the surface charge density. In other words the amount of charge per area. How can you use these ideas for your problem?
     
  6. Nov 6, 2009 #5
    The electric field inside a parallel plate capacitor:

    My book doesn't have that 2 in the denominator.
     
  7. Nov 6, 2009 #6
    Thank you. You are correct. The equation I gave was for the field due to a single plate. Since there are two plates superposition gives

    [tex]
    E = \frac{\sigma}{\epsilon_{0}}
    [/tex]

    for points internal to the plates.
     
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