Electric Field of Non-Conducting Sheets.

[dvsumosize]

Homework Statement

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

Homework Equations

The only 1 i know of is E = Sigma/(2*εnot)

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.

 

[supratim1]

electric fields are added as vectors. just add them with sign.

 

[SammyS]

Use Gauss's Law.

 

[dvsumosize]

Which formula from that law will i use, the only one i know is the E = Sigma/(2 * e-not)

 

[SammyS]

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

 

[dvsumosize]

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]

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

 

[supratim1]

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

 

[dvsumosize]

I see.

 

[supratim1]

so did you get the answer?

 

[dvsumosize]

yeah

 

[1994Bhaskar]

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!