Electric Field of Non-Conducting Sheets.

  1. 1. The problem statement, all variables and given/known data

    3 Infinitely large non conductiong sheets are uniformly charged with surface charge densities Sigma1 = +2x10^-6c/m^2, Sigma2 = +4x10^-6c/m^2, Sigma3 = -5.0x10^-6c/m^2. Distance L = 1.6cm. What is the magnitude and direction of the net electric field at point P?




    * P
    | L/2
    ________________ Sigma3
    |
    |
    | 2 *L
    |
    ________________ Sigma2
    | L
    |
    ________________ Sigma 1


    2. Relevant equations
    The only 1 i know of is E = Sigma/(2*╬Ánot)


    3. The attempt at a solution

    Es1 + Es2 + Es3 = Etot at P.




    So my teacher never really taught us about non-conducting sheets over any distance, and instead told us to google it and ask on forums instead. Please me through how you do this, i can't find a formula that deals with distance between non-conducting sheets.
     
  2. jcsd
  3. supratim1

    supratim1 280
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    electric fields are added as vectors. just add them with sign.
     
  4. SammyS

    SammyS 8,432
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    Use Gauss's Law.
     
  5. Which formula from that law will i use, the only one i know is the E = Sigma/(2 * e-not)
     
    Last edited: Mar 23, 2011
  6. SammyS

    SammyS 8,432
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    That's a result which can be obtained from Gauss's Law.

    Gauss's Law: [tex]\oint_S\vec{E}\cdot d\vec{A}=\frac{q_{inside}}{\epsilon_0}[/tex]
     
  7. Cramster tells me what i did at the beginning was right, distance doesn't matter in this case. Why did none of you tell me so?
     
  8. SammyS

    SammyS 8,432
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    It's rather hard to read your mind well enough to know what you do & don't understand.
     
  9. supratim1

    supratim1 280
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    distance doesn't matter here, as electric field is independent of distance for uniformly charged infinite sheet.
     
  10. I see.
     
  11. supratim1

    supratim1 280
    Gold Member

    so did you get the answer?
     
  12. yeah
     
  13. the same formula sigma/(2epsilon) can be obtained as follows:
    A Gaussian surface in the form of cylindrical surface can be taken.The field is perpendicular to sheet so only end caps contribute to flux.
    =>(epsilon)*(sufaceintegral(E.dA))=q

    =>(epsilon)*(EA+EA)=sigma*A
    =>(epsilon)*(2EA)=sigma*A

    canceling A from both sides & rearranging:

    =>E=sigma/(2*epsilon)

    Thus for a very large non-conducting sheet distance doesn't matter at all!what matters is sigma.so just as per vectors the electric fields depending upon nature of charge(positive or negative).If negative sigma then E is generally taken as negative(however you can take anything!!!).So the data regarding distance is irrelevant here!!!
     
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