Gauss' law which formula to use

[teknonjon]

Homework Statement

how do I know which equation to use for electric field? E=a/2e0 or E=a/e0 when a = surface charge density.

Homework Equations

The Attempt at a Solution

 

[cupid.callin]

first one is for single surface of a charged sheet ... when it is accompanied by another it changes to the second one (therefore it is twice of it)

 

[teknonjon]

I looked in my physics book and they use the formula E=a/2e0 when there is only one nonconducting sheet. The picture they show is a cylinder which is the Gaussian surface going through the sheet with both ends outside of the sheet. When they use the formula E=a/e0 half of the Gaussian surface is within the sheet so only one end of the cylinder is sticking ouside the sheet. I don't understand how making the changing the Gaussian surface like this would result in one answer for the electric field being only half the other. Shouldn't the electric field be the same no matter what you use for the Gaussian surface?

thank you for your reply earlier

 

[SammyS]

What is the electric field within a conducting material?

 

[rwisz]

Gauss' law is a fundamental law in electromagnetism that relates the electric field to the distribution of electric charges. It states that the electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space (ε0).

In order to determine which equation to use for the electric field in a given situation, it is important to first understand the properties of the surface charge density (a). If the surface charge density is uniform, meaning it is the same throughout the surface, then the equation E=a/2ε0 should be used. This is known as the Gaussian surface method, where the electric field is calculated by considering the flux through a hypothetical Gaussian surface surrounding the charge distribution.

If the surface charge density is not uniform, meaning it varies at different points on the surface, then the equation E=a/ε0 should be used. This is known as the differential form of Gauss' law, where the electric field is calculated by integrating over the surface charge density.

In summary, the equation to use for the electric field depends on the uniformity of the surface charge density. If it is uniform, use E=a/2ε0, and if it is not uniform, use E=a/ε0. It is important to carefully consider the properties of the charge distribution and choose the correct equation to ensure accurate results.