Gauss' Law and a uniform surface charge

In summary, to find the electric field inside and outside of a long hollow cylindrical tube with uniform surface charge sigma, one can use Gauss' Law. Inside the tube, the electric field is zero for all points. Outside the tube, at a radial distance of r from the tube of length L, the electric field is given by E = sigma/2πrε0, where σ is the surface charge density and ε0 is the permittivity of free space. This result is correct according to Gauss' Law.
  • #1
stunner5000pt
1,461
2
Use Gauss' Law to find the field inside and outside a long hollow cylindrical tube which carries a uniform surface charge sigma.

It has been a few months since i did this so i may be a bit rusty

As i can recall if there is a point inside a holow cylindrical tube there is no enclosed charge, hence the electric field is zero inside the tube for all points inside

for the outside
For a radial ditance of r from the tube of length L
[tex] \vec{E} d(2 \pi \vec{r} L) = \frac{\sigma L}{\epsilon_{0}} [/tex]

hence [tex] \vec{E} = \frac{\sigma}{2 \pi r \epsilon_{0}} \hat{r} [/tex]

is this fine??

thank you in advance for the help!
 
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  • #2
You got the right results.
 

FAQ: Gauss' Law and a uniform surface charge

What is Gauss' Law?

Gauss' Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the net electric charge enclosed by that surface. 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.

What is a uniform surface charge?

A uniform surface charge is a distribution of electric charge on a surface that is evenly spread out, meaning that the charge density (amount of charge per unit area) is the same at all points on the surface.

How is Gauss' Law used to calculate the electric field for a uniform surface charge?

Gauss' Law can be used to calculate the electric field for a uniform surface charge by applying it to a Gaussian surface that encloses the charge distribution. The electric flux through this surface can then be calculated and equated to the product of the enclosed charge and the permittivity of free space. This allows for the electric field to be determined at any point on or outside of the surface.

Can Gauss' Law be used for non-uniform surface charge distributions?

Yes, Gauss' Law can be used for non-uniform surface charge distributions as long as the charge distribution is known and the Gaussian surface can be properly chosen to enclose the charge. In this case, the electric field can be calculated at a specific point or integrated over a certain region to determine its overall effect.

What are some real-life applications of Gauss' Law and uniform surface charge?

Gauss' Law and uniform surface charge have various real-life applications, including calculating the electric fields of charged conductors, determining the electric potential of charged surfaces, and understanding the behavior of electrically charged fluids. They are also used in designing electronic devices, such as capacitors and transistors, and in studying the behavior of plasma in fusion reactors.

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