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Finding the E-field between two infinite plane charged sheets

  1. Jul 11, 2011 #1
    1. The problem statement, all variables and given/known data

    Two infinite-plane non-conducting, thin sheets of uniform surface charge p1 = 13.35 uC/m2 and p2 = -8.65 uC/m2) are parallel to each other and d = 0.245 m apart. (As shown in the diagram below.) What is the electric field between the sheets? (Note: the field is positive if it is parallel to the vector x).

    prob18a.gif

    2. Relevant equations

    Sigma/2*epsilon_not

    Epsilon not = 8.85e-12 (SI Units)

    3. The attempt at a solution

    The distance between the sheets should not matter in calculating the E-field between them because the E-field between them is uniform. We are given two sigmas and since the net charge on the field is toward the negative plane we just sum the two over 2*epsilon_not, and Epsilon not is a constant.

    sigma1=13.35e-6 C/m^2
    sigma2=-8.65e-6 C/m^2

    (sigma1 + sigma2)/(2*epsilon_not) = E-field
    (13.35e-6 + 8.65e-6)/(2*epsilon_not) = 1.2e6 N/C
    Than since the E-field is perpendicular to the planes, but pointing in the opposite direction of positive X the answer becomes negative.
    Answer: -1.2e6 N/C (unfortunately I tried this and did not get the problem right)

    What did I get wrong?
     
  2. jcsd
  3. Jul 11, 2011 #2

    SammyS

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    In the region between the sheets:
    What is the direction of the E field due to the σ1 sheet?

    What is the direction of the E field due to the σ2 sheet?​
     
  4. Jul 11, 2011 #3
    The E-field on sigma1 is going -x and so is sigma2 right?
     
  5. Jul 11, 2011 #4

    gneill

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    Is the marking software fussy about significant figures?
     
  6. Jul 11, 2011 #5

    SammyS

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    Right, so you should have a negative plus a negative.
     
  7. Jul 12, 2011 #6
    Right but that doesn't change the answer numerically am I forgetting a step?
     
  8. Jul 12, 2011 #7

    Doc Al

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    Why did you express your answer to only 2 sig figs? (To repeat what gneill already pointed out.)
     
  9. Jul 12, 2011 #8
    More sig figs worked thank you everyone!
     
  10. Jul 12, 2011 #9

    SammyS

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    You have:
    E-field due to sigma1=13.35e-6 C/m2
    E-field due to sigma2=-8.65e-6 C/m2


    But, if they're both pointing left (as vectors), then they should both be negative !

    E1 + E2 = -13.35×10-6 + -8.65×10-6 = ____ ?
     
  11. Jul 12, 2011 #10
    yes thats the way I ended up doing it -13.35e-6+-8.65e-6
     
  12. Jul 12, 2011 #11

    SammyS

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    That's stange, I don't see that result anywhere in this thread.
     
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