Charge density...electric field...electric potential
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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)
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Solution Summary
The expert examines charge density, electric field and electric potentials. The total charge enclosed in a cylinder gaussian surface is given.
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This is like a co-axial cable, however just note that we have to speak of charge density per unit length, not total charge density.
(A) In a length l of the cylinders we have a volume of
V = Pi (b^2-a^2)l
The total charge will be
Q= 4 Pi (b^2-a^2) l p0 [ read "rho sub zero"!]
And the linear charge density will be
4 Pi (b^2-a^2) p0
and the charge density itself will be zero in the very inner layer, p0 in between and zero again ...
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