# Gauss's law for a cylinder

1. Dec 2, 2009

### 1st2fall

1. The problem statement, all variables and given/known data
Suppose that the inner cylinder of the figure below is made of nonconducting material and carries a volume charge distribution given by ρ(R) = C/R, where C = 301 nC/m2. The outer cylinder is metallic and both cylinders are infinitely long.

a.Find the charge per unit length (that is, the linear charge density) on the inner cylinder.

b.Calculate the electric field for all values of R.

2. Relevant equations
$$\Phi$$=$$\frac{Q}{\epsilon_0{}}$$

3. The attempt at a solution
a. I'm not quite sure how to find the linear charge density given the density for the volume which is in turn as a Area-density by the radius..... it looked like a big conversion mess. I tried multiplying by .03m to see if that worked but apparently that's along the wrong lines of thinking. This is very basic but I'm just looking to see the relation between the linear and area density.

b.I would have thought that the metallic cylinder acted as a Faraday cage and would prevent charge from leaking through the outside but apparently that's not so. Also it mentioned that the inner rod is nonconducting so I am not sure whether the relation for uniform charge distribution inside a material still holds... if it does then the math i did earlier was wrong. I am confused as to why there is no field in the cylinder but there is on the outside of it??? any clarification would be greatly appreciated. Numbers aren't exactly what I'm asking for I just want to understand the relationship for the feilds in the cylinder and rod.

thank you very much for any and all help

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