# Cylindrical Shell (Electromagnetism Physics)

1. Feb 2, 2005

### jmerickson

Cylindrical Geometry in End View

An infinite, uniform line charge with linear charge density l = +5 µC/m is placed along the symmetry axis (z-axis) of an infinite, thick conducting cylindrical shell of inner radius a = 2 cm and outer radius b = 5 cm. The cylindrical shell has zero net charge.

The electrical potential is chosen to be zero at the outer surface of the cylindrical shell, V(b) = 0. (In this problem, it is not possible to chose the potential to be zero at infinity because the charge distribution extends to infinity.)

(a) Calculate the potential at a radial distance r = (a+b)/2 (measured perpendicularly from the z-axis).
V((a+b)/2) = 0 V

(b) Calculate the potential on the inner surface of the cylindrical shell.
V(a) = 0 V

(c) Calculate the potential at a radial distance r = a/2.
V(a/2) = ? V

HELP: Identify the equivalent line charge problem that has the same electric field in the region r < a as the specified charge distribution.
HELP: Find the potential that corresponds to the equivalent line charge, including an arbitrary additive constant. Fix the additive constant by using your answer to the previous part.

(d) Calculate the potential at a radial distance r = 2b.
V(2b) = ? V

HELP: Identify the equivalent line charge problem that has the same electric field in the region r > b as the specified charge distribution.
HELP: Find the potential that corresponds to that equivalent line charge, including an arbitrary additive constant. Fix the additive constant by using known information.

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im stuck on c and d and i have no idea where to start

2. Feb 2, 2005

### jmerickson

i guess i dont have a clue what they are saying about the additive constant.

the electric field of a line of charge is lamda/(2*pi*(epsilon zero)*r) where lamda is the charge density of the line of charge epsilon zero is 8.85x10^-12 and r is the distance from the line of charge perpendicular to the z-axis. i can see there is something you have to do to integrate it. do you pull out the lamda/(2*pi*(epsilon zero)) and integrate 1/r and go from there?