Finding the E-field between two infinite plane charged sheets

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  • #1
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Homework Statement



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


Homework Equations



Sigma/2*epsilon_not

Epsilon not = 8.85e-12 (SI Units)

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?
 

Answers and Replies

  • #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?​
 
  • #3
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The E-field on sigma1 is going -x and so is sigma2 right?
 
  • #4
gneill
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Is the marking software fussy about significant figures?
 
  • #5
SammyS
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The E-field [STRIKE]on[/STRIKE] due to sigma1 is going -x and so is sigma2 right?
Right, so you should have a negative plus a negative.
 
  • #6
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Right but that doesn't change the answer numerically am I forgetting a step?
 
  • #7
Doc Al
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Right but that doesn't change the answer numerically am I forgetting a step?
Why did you express your answer to only 2 sig figs? (To repeat what gneill already pointed out.)
 
  • #8
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More sig figs worked thank you everyone!
 
  • #9
SammyS
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Right but that doesn't change the answer numerically am I forgetting a step?
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 = ____ ?
 
  • #10
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yes thats the way I ended up doing it -13.35e-6+-8.65e-6
 
  • #11
SammyS
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That's stange, I don't see that result anywhere in this thread.
 

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