A long straight conducting rod (orwire) carries a linear charge density of +2.0

Question

A long straight conducting rod (orwire) carries a linear charge

densityof +2.0C/m. This rod is totally enclosed within a thincylindrical

shell of radius R, which carries alinear charge density of - 2.0C/m.

A) Describe how you would constructtwo Gaussian surfaces to calculate the

electric field: one outside thecylindrical shell, and the

other between the shell and the wire,to apply Gauss’ Law

B) Write the expression for theelectric flux threading each of your Gaussian

surfaces and for the resulting electric fieldin each region

Explanation / Answer

Q = L     charge on length L ofinner wire = Q / 0     flux due to "enclosed" charge Construct imaginary cylinder of radius R inside cylinder E A = = Q / 0 = L /0 E =   L / (0 2 R L) = / (0 2 R)       field at distance R fromcentral wire inside of outer cylinder Outside the cylinder the net enclosed charge is zero and thefield is zero E =   L / (0 2 R L) = / (0 2 R)       field at distance R fromcentral wire inside of outer cylinder Outside the cylinder the net enclosed charge is zero and thefield is zero

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