Chapter 23, Problem 028 A charge of uniform linear density 3.00 nC/m s distribut

Question

Chapter 23, Problem 028 A charge of uniform linear density 3.00 nC/m s distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 5.40 cm outer radius 11.0 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r 16.4 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell? unthorshellis zero. (a) What is the magnitude of the el Gansian cylnder (a) Number (b) Number (c) Number Units Units Units

Explanation / Answer

Given,

linear density along the rod, = 3 x 10-9 C/m

a)if L is the length then the charge associated, q= 3 x 10-9 x L C

using Gauss law the electric field at a point r = 0.164 is

E= q/ 2rLo = 3 x 10-9/ (2 x x 0.164 x 8.85 x 10-12) = 328.97 N/C

b) surface charge density on the inner surface, = -/2ri = -(3 x 10-9)/ 2(0.054) = -8.84 nC/m2

c) surface charge density on the outer surface, = /2ro = -(3 x 10-9)/ 2(0.11) = 4.34 nC/m2

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