An infinite,uniform line charge with linear charge density l = +2 µC/m is placed

Question

An infinite,uniform line charge with linear charge density l = +2 µC/m is placed along the symmetryaxis (z-axis) of an infinite, thick conducting cylindricalshell of inner radius a = 2 cm and outer radius b= 3 cm. The cylindrical shell has zero netcharge.

The electricalpotential is chosen to be zero at the outer surface of thecylindrical shell, V(b) = 0. (In this problem, itis not possible to chose the potential to be zero at infinitybecause the charge distribution extends toinfinity.)

(a) Calculatethe potential at a radial distance r =(a+b)/2 (measured perpendicularly from thez-axis).

V((a+b)/2) =V    *
0   OK

HELP:  Whatgeneral principle applies to the potential at various points in aconductor?

(b) Calculate the potential on the innersurface of the cylindrical shell.

V(a) =V    *
0   OK

(c) Calculate the potential at a radialdistance r = a/2.

V(a/2) =V    *
24919   OK

(d) Calculate the potential at a radialdistance r = 2b.

V(2b) =V    
45037   NO

Explanation / Answer

the cylindrical shell is uncharged but conducting when you place a charge at the center () it will attractelectrons (charge) to the inner surface of the shell; the net charge of the shell must remain zero, thuspositive charge accumulates accordingly at the outer surface now determine V at 2b

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