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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)

Solution Preview

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.
<br>(A) In a length l of the cylinders we have a volume of
<br> V = Pi (b^2-a^2)l
<br>The total charge will be
<br> Q= 4 Pi (b^2-a^2) l p0 [ read "rho sub zero"!]
<br>And the linear charge density will be
<br> 4 Pi (b^2-a^2) p0
<br>and the charge density itself will be zero in the very inner layer, p0 in between and zero again ...