Gauss's law on a charged sheet.

In summary, the conversation discusses finding the field produced by a uniformly charged sheet with a charge density of 87 pC/m2. The equations used are the electric flux equation and the equation for electric field due to a charged sheet. The attempted solution results in an answer of 4.92 N/C, but the book states the answer as 49 kN/C, suggesting a possible error in the given charge density.
  • #1
pondzo
169
0

Homework Statement



find the field produced by a uniformly charged sheet carrying 87 pC/m2

Homework Equations



[itex]\oint \vec{E}.d\vec{A}[/itex] = qenclosed/[itex]\epsilon[/itex]

The Attempt at a Solution



[itex]\Phi[/itex]= [itex]\sigma[/itex]A/[itex]\epsilon[/itex]
[itex]\Phi[/itex]=[itex]\oint E.dA[/itex] = ## E(2A) ##

2EA= [itex]\sigma[/itex]A/[itex]\epsilon[/itex]
E = [itex]\sigma[/itex]/(2[itex]\epsilon[/itex]) = 4.92 N/C where I use 8.85*10-12 for [itex]\epsilon[/itex] (this has been the value used through the book)
However the book says the answer is 49 kN/C
could someone point out my error? Thanks.
 
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  • #2
Your answer looks OK to me. What book are you using?
 
  • #3
Since you are off (from the book's answer) by 104, I wonder if the charge density was meant to be in pC/cm2, not pC/m2.
 
  • #4
I'm using Richard Wolfson's: essential university physics 2nd edition, ch 21 qn 33.
 
  • #5
yeah that might be the problem, as i have seen similar qns to this one online but they use pC/cm^2 instead of pC/m^2
 

Related to Gauss's law on a charged sheet.

1. What is Gauss's law on a charged sheet?

Gauss's law on a charged sheet is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed within that surface. It states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.

2. How is Gauss's law on a charged sheet different from Gauss's law for a point charge?

Gauss's law on a charged sheet applies to a two-dimensional surface, while Gauss's law for a point charge applies to a three-dimensional volume. Additionally, Gauss's law on a charged sheet uses the concept of surface charge density, while Gauss's law for a point charge uses the concept of point charge.

3. What is the significance of Gauss's law on a charged sheet?

Gauss's law on a charged sheet is significant because it is a powerful tool for calculating electric fields in situations with high symmetry, such as infinite sheets or cylinders. It also helps us understand the relationship between charge and electric fields.

4. How is Gauss's law on a charged sheet applied in practical situations?

Gauss's law on a charged sheet can be applied in various practical situations, such as calculating the electric field of a parallel plate capacitor or a charged metal plate. It is also used in the design of electric circuits and in understanding the behavior of lightning.

5. Are there any limitations to Gauss's law on a charged sheet?

One limitation of Gauss's law on a charged sheet is that it only applies to situations with high symmetry. It also assumes that the electric field is uniform over the surface of the sheet. Additionally, it does not take into account the effects of other nearby charges or external electric fields.

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