Proof of Electric Field Zero Inside Cylindrical Shell: Coulomb's Law

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Given an infinite long cylindrical shell of inner radias a and outer radius b.

proof using coulombs law that any point inside the inner radius a, the eletric field will always be zero.
 
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It's easy enough using Gauss's law. Coulomb's law is a little more difficult.

Of course, this assumes the cylinder is a conductor. If it isn't, the statement isn't necessarily true.
 
well, there is no fun if it is easy.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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