A nonconducting infinite cylindrical shell of inner radius a

A non-conducting infinite cylindrical shell of inner radius a and outer radius b has a positive and uniform volume charge density ?. Which of the following graphs best represents the magnitude of the electric field as a function of radial distance from the center of the shell?

QUESTION 9 A non-conducting infinite cylindrical shell of inner radius a and outer radius b has a positive and uniform volume charge density . Which of the following graphs best represents the magnitude of the electric field as a function of radial distance from the center of the shell? 0 2 0 3 a b

Solution

Applying Gauss law, ( Considering concetric sphere of radius r as gaussian surafce)

then E. A = Qin / e0

for r < a

Qin = 0

for a < r < b

Qin = rho [(4 pi r^3 / 3) - (4 pi a^3 / 3)]

E ( 4 pi r^2 ) = rho [(4 pi r^3 / 3) - (4 pi a^3 / 3)] / e0

E = rho ( r^3 - a^3) / 3e0

for r > b

Qin will be constant say Q.

Q = 4 pi rho (b^3 - a^3) / 3

E (4 pi r^2 ) = 4 pi rho (b^3 - a^3) / 3e0

E = (rho ( b^3 - a^3)/3e0) / r^2

hence graph will be Option 4.