PART A: Physics 2135 Special Homework Assignment #3 An infinitely long insulatin

Question

PART A:

Physics 2135 Special Homework Assignment #3 An infinitely long insulating cylindrical she has an inner radius a, an outer radius b, and an unknown uniform positive charge density p (charge per unit volume distributed in the region between r a and r b. (a) Using Gauss's law, find the electric field in the hollow inner region r a. Begin with a statement of Gauss's Law and justify all steps leading to your answer. (b) Suppose the electric field at the outer edge of the cylindrical shell (i.e., at r b) is measured, and is found to have a magnitude of Eo. Use Gauss's law to express the charge density p in terms of the quantities Eo, a, b, and any fundamental constants you may need. Leave your answer in symbolic form. (c) Find the magnitude E of the electric field at a radial distance a

Explanation / Answer

(A) considering a conectric cylinder of radius r and length L as Gaussian surface.

given cylinderical shell is infinitly long hence field through flat circular part will be zero.

and field through curved part will be constant at radius r say E.

Gauss' Law,

total flux = Qinside / e0

for r < a

Qin = 0

E . (2 pi r L) = 0 / e0

E = 0

(B) for r = b

Qin = rho pi (b^2 - a^2) L

Eo ( 2 pi b L) = rho pi (b^2 - a^2) L / e0

Eo = (rhp (b^2 - a^2)) / (2 e0 b)

rho = ( 2 e0 b Eo) / (b^2 - a^2)

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