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Homework Help: Finding E and V involving 2 planes.

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Two large planes have uniform charge density. Plane 1 is located at z1=-4 cm and has charge density σ1=-10μC/cm2. Plane 2 is located at z2=+6 cm and has charge density σ2=+20μC/cm2.
    a. Determine E(x,y,z) in the 3 regions.
    b. Determine V for all points. Choose V=0 at plane 2.
    c. Briefly describe the equipotentials, draw and label at least 3 of them.

    2. Relevant equations



    3. The attempt at a solution

    I know that Gauss Law has to be used. I am just a bit confused on the concept that the charge distributions aren't equal. This is throwing me off a little bit. Do I find the Q-enclosed for both individually, then add them?
     
  2. jcsd
  3. Sep 18, 2010 #2

    kuruman

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    Yes, you calculate the E-field from each plate separately (as if the other one were not there) and then add the fields vectorially in each of the three regions. That's what "superposition" means.
     
  4. Sep 18, 2010 #3
    I got E=10uC/2epsilon-naught for between the plates, E=-10uC/2epsilon-naught for the upper plane, and E=20uC/2epsilon-naught for the bottom plate. Does this seem correct? I am still a tad confused.
     
  5. Sep 19, 2010 #4
    I tried to think of this in other manners, but wasn't successful. Any thoughts are welcome. Thanks again.
     
  6. Sep 19, 2010 #5

    kuruman

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    This does not seem correct. Start with E = σ/(2ε0) and list separately the values of the field E1 in each of the three regions and of E2 in each of the three regions (6 numbers altogether). It would help if you drew a picture and don't forget that field lines go towards the negatively charged plate on both sides and away from the positively charged plate on both sides.
     
  7. Sep 19, 2010 #6
    Hmm this is what I attempted to do. I have attached my work to this post to see if you can give me some pointers as to where I made a mistake. Thanks.

    Edit: I don't know why the picture is rotated. It's not like that when I upload it. Sorry.
     

    Attached Files:

  8. Sep 19, 2010 #7

    kuruman

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    I do not understand the arrows that you have drawn in the figure. Draw two arrows, no more no less, side by side in each region to represent the fields contributed by each plate. Then we'll have something to talk about.
     
  9. Sep 19, 2010 #8
    The two plates should have have piecewise functions of E, in other words, E for left of the plate, and E for right of the plate. Try doing that to get the electric fields right, and then your superposition should follow. Your magnitudes are right though.
     
  10. Sep 19, 2010 #9
  11. Sep 19, 2010 #10
    Mindscrape: what do you mean to the right and to the left of the plates? shouldn't it be to the top and bottom of them? Thanks.
     
  12. Sep 19, 2010 #11

    kuruman

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    The top plate is positively charged and the bottom plate is negatively charged. You have the arrows mixed up. Also in the in-between regions you have more than two arrows and have not labeled any of them, so it is not clear which arrow is contributed by which plate.
     
  13. Sep 19, 2010 #12
    Oh I had read the problem wrong. Ok I fixed the directions of my arrows. For the in-between regions I only have two arrows, the other lines are my coordinate axes. (the 'x' I drew is the origin.) I hope this makes it easier to follow.

    Should I draw four arrows in the middle, even though they all point in the same direction? Two for each plate's contribution?
     
  14. Sep 19, 2010 #13

    kuruman

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    There are only two plates, so in each region there should be only two arrows, one from each plate.
     
  15. Sep 19, 2010 #14
    Ohh I think/hope I got it now. The right column of vectors are the contributions of the bottom plate. The left column are for the top plate.
     

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  16. Sep 19, 2010 #15
    Yeah, there you go. Yes, I did mean top and bottom earlier, I was looking at your sideways drawing. :)
     
  17. Sep 19, 2010 #16
    Haha ok good. So now, I draw 3 different Gaussian surfaces?
     
  18. Sep 19, 2010 #17

    kuruman

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    OK, so now put in the numbers and add the two arrows in each region. Don't forget that up is positive and down is negative.
     
  19. Sep 19, 2010 #18
    Ok I think I got part a. Any comments?
     

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  20. Sep 19, 2010 #19

    kuruman

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    No comments. Looks OK.
     
  21. Sep 19, 2010 #20
    Ok great. So for part b, do I take my values for E, and integrate over dz?
     
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