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Homework Help: Problem in orienting two plates as instructed in question

  1. Sep 15, 2015 #1
    1.The problem statement, all variables and given/known data
    Two large thin metal plates are parallel and close to each other. on their inner faces ,the plates have surface charge densities of opposites signs and magnitude 1.77 multiplied by 10^-11 coulomb per square meter.What is electric field
    a)to the left of the plates
    b)to the right of the plates
    c)in between the plates
    2. Relevant equations
    E=σ/2ε0

    3. The attempt at a solution
    What is the proper orientation when the question says Two large thin metal plates are parallel and close to each other
    I thought the following is correct
    plane.png

    But this is not correct.
    The answer is Fields due to both the plates will be equal and opposite so net field will be zero.I can not differentiate between the cases that are
    to the left of the plate (2) and between the plates
     
  2. jcsd
  3. Sep 15, 2015 #2

    TSny

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    In part (a), "to the left of the plates" refers to the far left region; that is, the region to the left of the left plate.
    Likewise in part (b), "to the right of the plates" refers to the far right region; that is, the region to the right of the right plate.
     
  4. Sep 15, 2015 #3
    Even if that's the case how come
     
  5. Sep 15, 2015 #4
    I mean
    Can electric field due to plate (2)go beyond the plate (1) i.e to the far left region
    or even if it can ;would the electric field intensity of the charges of plate 2 be equal to that of plate one there in order to cancel the effect?
     
  6. Sep 15, 2015 #5

    ehild

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    Imagine one plate: When it is positively charged, the field lines emerge from it, and point away from the plate at both sides.
    If the charge is negative, the field lines enter into the plate at both sides.
    You can substitute the plates by planar distributions of charges. Both planes have their field everywhere, as shown in the picture. The orange lines are due to the positive charges, the blue lines belong to the negative ones. Apply he Superposition Principle: the resultant field is the sum of the fields of the individual planes.

    twoplates3.jpg
     
  7. Sep 15, 2015 #6
     
  8. Sep 15, 2015 #7

    ehild

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    If the charges per unit surface area are equal, the fields are of equal magnitude.
     
  9. Sep 15, 2015 #8
    But electric field also depends on r i.e distance from source charge
     
  10. Sep 15, 2015 #9

    ehild

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    NO, if the plates are infinite (at least their lateral sizes are much larger than the distance between them). You wrote that E=σ/(2ε0) !
     
  11. Sep 15, 2015 #10
    YES .I wrote that but I did not understand.
     
  12. Sep 15, 2015 #11
    But it's beyond them not between them
     
  13. Sep 15, 2015 #12
     
  14. Sep 15, 2015 #13

    ehild

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    It is symmetry again. The charge is evenly distributed on the plane. At a point the fields of the individual charges add as vectors. The parallel components cancel and only the perpendicular components remain. As the plane is of infinite extension, the field is the same above each points. If you integrate the contribution of all charges you will get the same result, independently how far the point is from the plate.
     
  15. Sep 15, 2015 #14

    ehild

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    The field of an infinite plate with even surface charge distribution is the same at both sides, only of opposite sign.
     
  16. Sep 15, 2015 #15
    Ok.One more question If these are metal plates ,why charges are spread throughout the surface;charges should reside on borders/outer surface
     
  17. Sep 15, 2015 #16

    ehild

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    The plates were assumed of infinite sizes.
    Even in case of real metal plates, not all charge reside along the borders. But it is true that they are spread on the surfaces.
     
  18. Sep 16, 2015 #17
    Could you please elaborate this?
     
  19. Sep 16, 2015 #18
  20. Sep 16, 2015 #19

    ehild

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    I spoke about infinite plate.
     
  21. Sep 16, 2015 #20
    Isn't there a little similarity between the two cases i.e finite plane when electric field is taken at mid point and infinite plate
     
  22. Sep 16, 2015 #21
    I am not able to comprehend this.
     
  23. Sep 16, 2015 #22
    I am afraid ;It could be very silly question but I am serious about it.Will there be electric field intensity or force even when something comes in between(in the way of source charge to the point of interest) as in my question there is plate (1) in between the charges of plate 2(source charge) and the far left region but still electric field intensity is same as if nothing is in between.
     
  24. Sep 16, 2015 #23

    ehild

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    The superposition principle says that you can calculate the resultant field of several objects separately, as if the other objects were not there, and then sum the individual fields. One plate has its own field, the other one has its own field, too. And the field of two plates is the sum of these contributions.
     
  25. Sep 16, 2015 #24
    Exactly What I wanted.Thanks @ehild
     
  26. Sep 16, 2015 #25

    ehild

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    Watch this video
     
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