Question on a Gauss's Law problem

In summary, the conversation discusses the application of Gauss's Law to two problems. For question 007, the individual attempted to solve the problem by ignoring the outer shell and integrating the charge density over the inner cylinder. However, their solution was incorrect. For question 008, they calculated the total enclosed charge per unit height of the inner cylinder and divided it by the surface area of the inner surface, but this approach also led to an incorrect solution. The issue may lie in incorrectly using the expression ##\pi r^2## in the integrand for calculating the charge on the inner cylinder.
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Summary:: I understand the basics of Gauss's Law and how to solve some of the simpler problems, but I cannot seem to solve these two questions.

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For question 007, one of my friends told me I had to ignore the outer shell? I did that: I integrated rho dV: (6.02*r*pi*r^2*h) from r=0 to r=.0462 and set that equal to epsilon(naught)*E*2pi*0.188*h (this is: epsilon(naught) * the closed integral of E dA) and solved for E. Yet, this was incorrect.

For question 008, I calculated the total enclosed charge per unit height of the inner cylinder per meter by integrating rho dV from r=0 to r=.0462. I got something like q(enc)=0.00002154*h, so that means the charge of the inner surface of the hollow cylinder must be -0.00002154*h, right? I then divided that by the surface area of the inner surface, which was 2*pi*.117*h to get charge per unit area, yet, this was also incorrect.

Thanks in advance!
 
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dliu1004 said:
For question 007, one of my friends told me I had to ignore the outer shell? I did that: I integrated rho dV: (6.02*r*pi*r^2*h) from r=0 to r=.0462

So, your integrand for calculating the charge Q on a length ##h## of the inner cylinder is (including the ##dr##) $$(6.02 \frac{C}{m^4}) r \pi r^2 h dr$$

Note that overall, this does not have the units of charge since ##r \pi r^2 h dr## has units of ##m^5##. I think the problem is with the ##\pi r^2## part of your expression.

What is the volume of a thin cylindrical shell of inner radius ##r##, outer radius ##r+dr##, and length ##h##?
 
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