A co-axial cylinder is formed of two concentric thin conducting shells of infini

Question

A co-axial cylinder is formed of two concentric thin conducting shells of infinite length. One of radius R1, the other is of radius R2. (8 pts) R1 R2 Assume that the surface charge density on the inner shell is 1, and the surface charge density on the outer shell is 2. Coaxial cables are overall neutral, which means that for a certain length of the cable, the total charge on the inner cylinder must be equal to the total charge on the outer cylinder. Using this information, find the relation between 1 and 2

Explanation / Answer

given coaxial cylinder formed out of two thin concentric conducting shells of infinite length
inner radius = R1, surface charge density = sigma1
outer radius = R2, surface charge density = sigma2
also, overall neutrality of charger perunit length is there on the cable

so for length l
charge on outer wire = charge on inner wire
sigma1*2*pi*R1*l = sigma2*2*pi*R2*l
sigma1*R1 = sigma2*R2

hence
sigma1/sigma2 = R2/R1

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