Quick question, i think, link to problem included

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pyroknife
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Homework Statement


http://www.physics.wisc.edu/undergrads/courses/spring09/248/HWSolutions/HW6Solutions.pdf

My question regards to part b of the problem on the 1st page.

Why is the radius to get the charge density the radius of the outer sphere and not just the radius of the cylinder that's actually charged? Like when the radius is more than the radius of the inner cylinder, that means there's no charge right so shouldn't the maximum radius be 1.5cm in this case?
 
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Although the net charge of the outer shell is zero, there are charges on its surfaces, negative on the inner surface and positive on the outer one. The surface charge density is equal to ε0E (E is the magnitude of electric field at the surface).

ehild