How to calculate the flux given the surface charge density?

[kloong]

Homework Statement

Given long cylinder of radius 0.2m lies along the z-axis and carries a uniform surface charge density if 10m C/m2. Calculate the flux passing through a window at (rho) = 2m, pie/4 <= (phi) <= 3pie/4 , 2<=z<=4.

Homework Equations

The Attempt at a Solution

not sure where to start..

 

[Doc Al]

Consider Gauss's law and symmetry. (Try to picture the imaginary field lines that the charge distribution would produce.)

 

[kloong]

umm.. i still don't get it.. =(

 

[Defennder]

One of the symmetries you can exploit is assuming that there isn't any E-field component which isn't parallel to the x-y plane, since it's a long cylinder. So that means the flux through any closed cylindrical surface would be due only to the E-field in the a_rho direction. And since the surface charge density is uniform, E_rho should be a function of rho only.

 

[Troels]

You could find the explicit function for E and integrate it over the window, but that isn't necessary thanks to our old friend Gauss. Here's how I would do it:

1. Construct a cylindrical surface around the cylinder, with radius 2 and from z=2 to z=4
2. Calculate the total charge Q inside this surface
3. Invoke a symmetry argument (infinite z-dimension), to convince yourself that the E-field is everywhere perpendicular to the cylinder, so any flux through it is entirely through the curved surface and none at the plane ends.
4. Invoke Gauss law to find the total flux out though cylindrical surface
5. Invoke yet another symmetry argument (rotational symmetry) to convince yourself that the flux is uniform over the cylindrical surface
6. Find the flux through the window as a fraction of the flux through the whole surface.

 

[kloong]

i am so sorry.. but is it ok if u show me how to solve it and get the answer?

 

[Doc Al]

You give it a try. Troels gave you a set-by-step outline of how to proceed. If you have no idea about how to use Gauss's law, then you should spend your time reviewing that before attempting this problem. I'm sure your text has several examples worked out; so does this site: http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/gaulaw.html#c4".

 

[kloong]

ok. i will.