An infinitely long cylindrical insulating shell of inner rad

An infinitely long, cylindrical, insulating shell of inner radius a and outer radius b has a uniform volume charge density p. A line of uniform linear charge density 2 is placed along the axis of the shell. Determine the electric field in the following regions. (Choose a gaussian cylinder of radius r and length L. Use any variable or symbol stated above along with the following as necessary: ke) (a) r

Solution

(A) from Guass law,

E (2 pi r L) = Qin / e0  

r < a ; Qin = lambda L

E ( 2 pi r L) = lambda L / e0

E = lambda / (2 pi e0 r)

direction:- radially away from axis.

(B) a < r < b

Qin = (lambda L ) + (rho pi (r^2 - a^2) L )

E = (lambda / 2 pi e0 r) + (rho (r^2 - a^2)/ (2 e0 r))

away from axis

(C ) r > b;

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

E = (lambda / 2 pi e0 r) + (rho (b^2 - a^2) / (2 e0 r))

radially away from axis