# Electric Field of Non-Conducting Sheets.

1. ### dvsumosize

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.

280

3. ### SammyS

8,432
Staff Emeritus
Use Gauss's Law.

4. ### dvsumosize

12
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
5. ### SammyS

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

Gauss's Law: $$\oint_S\vec{E}\cdot d\vec{A}=\frac{q_{inside}}{\epsilon_0}$$

6. ### dvsumosize

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?

7. ### SammyS

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

8. ### supratim1

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

12
I see.

10. ### supratim1

280
so did you get the answer?

11. ### dvsumosize

12
yeah

135
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!!!