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Electric Field of Non-Conducting Sheets.

by dvsumosize
Tags: electric, field, nonconducting, sheets
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dvsumosize
#1
Mar23-11, 01:02 AM
P: 12
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*εnot)


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.
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supratim1
#2
Mar23-11, 01:07 AM
PF Gold
P: 280
electric fields are added as vectors. just add them with sign.
SammyS
#3
Mar23-11, 01:47 AM
Emeritus
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PF Gold
P: 7,801
Use Gauss's Law.

dvsumosize
#4
Mar23-11, 08:29 AM
P: 12
Electric Field of Non-Conducting Sheets.

Which formula from that law will i use, the only one i know is the E = Sigma/(2 * e-not)
SammyS
#5
Mar23-11, 06:24 PM
Emeritus
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PF Gold
P: 7,801
Quote Quote by dvsumosize View Post
Which formula from that law will i use, the only one i know is the E = Sigma/(2 * e-not)
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]
dvsumosize
#6
Mar24-11, 01:15 AM
P: 12
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?
SammyS
#7
Mar24-11, 01:52 AM
Emeritus
Sci Advisor
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PF Gold
P: 7,801
It's rather hard to read your mind well enough to know what you do & don't understand.
supratim1
#8
Mar24-11, 02:26 AM
PF Gold
P: 280
distance doesn't matter here, as electric field is independent of distance for uniformly charged infinite sheet.
dvsumosize
#9
Mar24-11, 09:43 AM
P: 12
I see.
supratim1
#10
Mar24-11, 10:52 AM
PF Gold
P: 280
so did you get the answer?
dvsumosize
#11
Mar24-11, 10:49 PM
P: 12
yeah
1994Bhaskar
#12
Apr10-11, 12:50 PM
P: 122
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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