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Homework Help: Find charge density on two parallel planes

  1. Aug 7, 2008 #1
    1. The problem statement, all variables and given/known data

    Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in region 1 to the left of plane A has magnitude 3σ/(2*ε0) and points to the left. The electric field in the region to the right of B has magnitude 3σ/(2*ε0) and points to the right. The electric field in the region between the the two planes has magnitude σ/(2*ε0) and points to the right. What is the surface charge density on planes A and B respectively?

    2. Relevant equations

    E = σ/(2*ε0)

    3. The attempt at a solution
    I have no idea where to begin. I was thinking that the charges were of magnitude 3σ, but that wouldnt explain the inside field...I just don't know how to think of this problem correctly...
  2. jcsd
  3. Aug 7, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    That's the correct formula for the field from one plane of charge. When you have more than one, you'll add up the field contributions from each. (The principle of superposition.)

    Hint: Don't forget that the direction (sign) of the field from a plane of charge is different on each side.
  4. Aug 7, 2008 #3
    adding up the field contributing from each? you mean that plate B is contributing to the field to the left of plate A, "region 1"? Well, I suppose it would have to be, I just don't see how. As for the superposition principle, I got that, since all these fields are on the same axis, I will just add or subtract them accordingly. But still...I have no clue how that formula works. Like I said, Using it on the left side of plane A tells you that the charge density is 3σ, which just isn't right...you get the same answer if you use it on plane B in the region to the right. But these charge densities clearly wouldnt get the E field we see in between the two planes...
  5. Aug 7, 2008 #4
    hah! Nevermind...I figured it out...you can get 2 systems of equations and solve for the 2 charge densities....

    Answer.. Plate A has charge density 2σ and B has charge density σ.

    Thanks much!
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