An infinite wire is a cylinder made out of a perfect conductor and has a Radius

Question

An infinite wire is a cylinder made out of a perfect conductor and has a Radius RA. The wire is concentrically covered by a perfectly conducting hollow cylinder of Radius RB (assume it is a very thin conducting shell). The outer cylinder is neutrally charged but has a uniform charge density of ?B = 0.5 C/m2 is measured on its outer surface. (RA = 2 cm, RB = 10 cm)

Please be clear and show all work

Very thin shell RB a) Because the outer cylinder is neutrally charged, what is the surface charge density ^ that MUST be on the wire? (hint ^ # b) What is expression for the electric field inside the outer cylinder a distance r from the center axis? Find E for RA

Explanation / Answer

a) the linear charge density is inversely proportional to the radius of the surface curvature.

therefore, the surface charge density = (10/2) * 0.5 C/m2 = 2.5 C/m2

b) by Gauss Law, E.2*pi*r = sigmaA/e, => E = sigmaA/(2*pi*e*r)

c) V = - Integral {E(r).dr} |Ra-->Rb = - sigmaA/(2*pi*e) * ln(Rb/Ra)

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