Charge density...electric field...electric potential
A (infinitley long) cylindrical non-conducting tube, inner radius a and outer radius b, with charge density p0 sits in a vacuum. Find (show work and derive) and sketch a plot as a function of radius r:
A) the charge density
B) the total charge enclosed in a cylindrical gaussian surface of radius r
C) the electric field
D) the electric potential referenced to the axis (r=0)© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/physics/electricity-magnetism/charge-density-electric-field-electric-potential-3i0
(B) The total charge enclosed will depend on the radius "r", we have three cases:
(i) r<a: Then charge enclosed is ZERO.
(ii) a<r<b: Charge will be contained between a layer of radius r and the inner layer of radisu "a":
Q = Pi (r^2-a^2) l p0
(iii) r>b: Then charge will be independent of r:
Q = Pi (b^2-a^2) l p0
again note the "l" that is dropped from the problem, but is implicit I guess!
(C) Using the Gauss' law we ...