Surface charge of an elliptical tube

[zabzab]

Homework Statement

An electric charge q is uniformly dispersed over a surface of elliptical tube with major and minor axis a and b. What is the surface charge density?

Homework Equations

The Attempt at a Solution

I I know that you have to cut the tube into thin ellipses and calculate a linear charge density for an ellipse. Than you sum the thin ellipses together to get a surface charge density of a tube. But I do not know how to calculate a linear charge density of an ellipse.

 

[voko]

If charge q is dispersed uniformly over a surface with area A, what is the surface charge density?

 

[zabzab]

Thank you for your quick replay voko. Ok, I see your point. Then I did not use the right word (lost in translation). I want calculate the areal charge density of an elliptic tube if we charge it and let the charge disperse on its own. I don’t think that we get the uniform charge density.

 

[voko]

Shall we assume that the tube is a conductor?

 

[zabzab]

Ow, of course.

 

[voko]

So you have a conducting tube (cylinder) whose cross-section is elliptical. The length of the tube is l, the ellipse's semi-major axes are a and b. Charge q is placed on the tube. Find the distribution of the charge on the tube.

How would you approach this?

 

[zabzab]

The distribution along the length of the tube is uniform if we consider a very long tube. So we can calculate a linear charge density of a thin elliptic slice and simply multiply that with the length of the tube. Here is where I have a problem. How to calculate a linear charge density of an elliptic slice.

I assume that the electric field inside is zero. Because the opposing sides of the ellipse cancel each other out. Now I don’t now haw to continue.

 

[haruspex]

If you're quite sure it is supposed to be a conducting shell, this link should help: http://www.hep.princeton.edu/~mcdonald/examples/ellipsoid.pdf, even though it's for an ellipsoid.
But I harbour a suspicion that the original form of the question is correct, and therefore solved as per voko.