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

here

total charge on Hollow cylinder is zero

thus (sigma B) *(2pi Rbl) + ( sigma A * 2pi RA *l) = 0

0.5 *10 + (sigma A * 2 cm) = 0

Sigma A = 0.1 C/m^2

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part B :

Apply Gauss law

E*(2 pi rL) = Qin/eo

E = sigmaA * 2 Pi Ra L/eo

E = (sigmaA *Ra)/eo r (ANSWER)

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part C:

dV = integral of sgmaA RA /eor

dV = sigma A RA /eo *(1/Ra - 1/Rb)

dV = (0.1*0.02)/(8.854 *10^-12) *(1/0.02-1/0.1)

V = 9 *10^9 Volts (answer)

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