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Homework Help: Electric field between two plates

  1. Jul 9, 2010 #1

    1. Positive and negative charges are distributed evenly in two parallel plates with width "w". The density of the positive and negative charge is +[tex]\rho[/tex] and -[tex]\rho[/tex]. Assume that the length of the plates at y direction is [tex]\infty[/tex]

    (a) Find the electric field in the plates
    (b) Let the electric potential at x=-w equal to 0, find the electric potential in the plates.

    2. Relevant equations
    [tex]\Delta[/tex]E=k*Delta-Q*r/r2 where r is the unit vector -- (1)

    3. My approach
    I sliced an infinitesimal portion of the plate horizontally denoted as Delta-y and represent the charge Delta-Q = rho *Delta-y*2*w. Is my expression for Delta-Q correct?

    r is the observation point which is at opposite to the portion Delta-y on the negative plate of which magnitude is "w".

    Substitute my expression for Delta-Q into (1), I obtain Delta-E = k*rho/w.

    Do I have to integrate Delta-E from -infinity to +infinity to obtain the electric field in the plates? If so, I will get E=0. Does this make sense?

    Thank you.
    Last edited: Jul 9, 2010
  2. jcsd
  3. Jul 9, 2010 #2


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    This is a Gauss's Law problem. Use the standard "pillbox" with its faces perpendicular to the x-axis.
  4. Jul 9, 2010 #3
    I obtained [tex]\rho[/tex]*2w/vacuum permittivity. I also did a sanity check that the unit is correct.

    Thanks for the guidance. Now I learnt that for highly symmetric problem, Gauss's Law really makes the problem much easier than using Biot-Savart Law.
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