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Electricity and Magnetism (Charged Plates)

  1. Nov 12, 2009 #1
    First year studying Physics at university.
    I've got my first E&M assignment and it's about charged plates but the thing is, I'm certain we haven't covered most of what it is asking, and I can hardly find any (simple) explanations to what I'm meant to do or methods I'm meant to use.

    I wasn't sure weather to put it here, or in homework, so if I'm wrong, sorry :( (Reason being that I don't really want specific help with the homework but more about the topic itself).

    I'll start with the first question first :P
    It is relatively straight forward (I think, unless it's more complex than I'm thinking).
    It says two metal plates of a thickness (let's just say [tex]l_a[/tex] for length of plates) separated by a distance [tex]z[/tex] with a P.D of [tex]V[/tex]. Ignoring edge effects calculate the charges and electric fields within the system. Plot a graph of charge density against position across the back of one plate to the back of the other. Hence draw a graph of electric field against position over the same range.

    So here's what I attempted/need explaining to me (please tell me if I'm wrong anywhere):

    To calculate the Electric field I would use this:
    [tex]E=\frac{V}{d}[/tex] where [tex]d=z[/tex].

    Now, for the charges (I'm unsure about this part):
    In this case the plates would be infinite, no? So it would be charge density (charge per unit squared) instead of just plain charges.
    So to work out the charge density [tex]\sigma[/tex] I'd use
    [tex]E=\frac{|\sigma|}{2\epsilon_0}[/tex] - I'm not convinced about this though, why would it be over [tex]2\epsilon_0[/tex] ?

    Also if E is calculated from above, how does with work with
    [tex]\nabla\cdot E = \frac{\sigma}{\epsilon_0}[/tex]
    because surely that would mean that E = 0 if you partially differentiated it?

    As for the graphs they would look like this, no?
    (axes: both x are position, y1 is charge density with max at sigma and minimum at -sigma at positions labeled and y2 is electric field with maximum at E)
    q99uj.jpg
    I understand the graphs, but obviously not fully (I know why it becomes a box from the straight lines) - because I can't explain it! Why does charge only appear at the surface and not inside the plate itself?

    Would someone be able to help explain the theory behind this please? Then I can ask about question (ii)

    Thanks in advance!
     
  2. jcsd
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