it’s the second time I post this question! Please help me if you really know. (2

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it’s the second time I post this question! Please help me if you really know. (20%) Problem 5: An infinite conducting cylindrical shell of outer radius ri-0.10 m, surface charge density 0.25 pCm2 A thin wire, with linear charge density 1.1 C m, is inserted along the shells' axis. The shell and the wire do not touch and these is no charge exchanged between them. and inner radius r2 = 0.08 m initially carries a se 33% Part (a) What is the new surface charge density in microcoulombs per square meter, on the inner surface of the cylindrical shell? Grade Summary Deductions Potential 97% Submissions Attempts remaining: 19 sino coso tan) 7 89 HOME per attempt) detailed view cotan) asin acoso atan acotan sinh0 cosh tanh)cotanho 0. END ODegrees Radians BACKSPACEL CLEAR Submit Feetack give up! Ilin ts:-% deduction per hint. Hints remaining Feedback:-deduction per feedback. 33% Part (b) what is the new surface charge density, in microcoulombs per square meter, on the outer surface of the cylindrical shell? Feedback: is available 11.5 10 01-1.5E-6 X Attempts Remain 33% Part (c) Enter an expression for the magnitude of the electric field outside the cylinder E-(A( 2x O r ) ) + ( r1.00 r ) XAttempts Remain r > 01 m, in terms of , o ri, and co- Feedback: is available.

Explanation / Answer

part a:

charge on the thin wire will be reflected on the inner shell of the cylinder.

let length of the cylinder be L.

then total charge on the thin wire=L*lambda=L*1.1 uC

charge reflected on lower shell=-1.1*L uC

so new surface charge density added=charge/surface area

=-lambda*L/(2*pi*r2*L)

=-lambda/(2*pi*r2)

=-1.1*L/(2*pi*r2*L)

=-2.1884 uC/m^2

part b:

new surface charge density on outer surface=sigma+(lambda/(2*pi*r2))

=-0.25 uC/m^2+2.1884 uC/m^2

=1.9384 uC/m^2

part c:

total charge enclosed by a cylindrical shell of radius r and length L

=(sigma+(lambda/(2*pi*r2))*2*pi*r1*L

using Gauss’ law:

epsilon*E*2*pi*r*L=total charge enclosed

hence E=(sigma+(lambda/(2*pi*r2))*2*pi*r1*L/(2*pi*epsilon*r1*L)

=(sigma+(lambda/(2*pi*r2))*r1/(epsilon*L)

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