Surface charge of an elliptical tube

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Homework Help Overview

The problem involves calculating the surface charge density of an elliptical tube with a uniform charge distribution. The original poster attempts to understand how to derive the surface charge density from the charge distributed over the tube's surface, considering the geometry of the ellipse.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the need to calculate a linear charge density for an elliptical cross-section and how to sum these to find the surface charge density. There are questions about the assumptions regarding the tube being a conductor and the implications for charge distribution.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem, including the nature of the charge distribution and the assumptions about the tube's conductivity. Some guidance has been offered regarding the approach to calculating charge density, but no consensus has been reached.

Contextual Notes

There is uncertainty about the uniformity of the charge distribution and whether the tube should be treated as a conductor. Participants are also considering the implications of the tube's geometry on the charge distribution.

zabzab
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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.
 
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If charge q is dispersed uniformly over a surface with area A, what is the surface charge density?
 
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.
 
Shall we assume that the tube is a conductor?
 
Ow, of course.
 
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?
 
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.
 

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