Question

A conducting rod of radius R₁= 1 nm and length L=10 nm inside a thin-walled coaxial conducting cylindrical shell of radius R₂= 10R₁ with the same length L. Use Gauss’s Law (derive the formula) to find the electric field at point

“a” located 2R₂ mm beyond the surface of the shell.

“b” located 5R₁ mm within the surface of the shell.

Answer 1

From the Gauss law

EA = q_enclosed/ eo

here the charge enclosed by the gaussian surface is

q_enclosed = net charge on the rod + net charge on the shell

E( 2 pi rL) = q_enclosed/ eo

E = q_enclosed/ 2pi ( 2R2) eo L

= q_enclosed/ 2pi ( 2( 10 R1) eo L

= q_enclosed/ 40 pi R1 eoL

= q_enclosed / 40 ( 3.14) ( 1* 10^-3 *1* 10^-9) ( 8.85* 10^-12) ( 10* 10^-9)

= q_ enclosed/11115.6 * 10^-33

(b)

E( 2pi rL) = q_enclosed/ eo

E = net charge on the rod/ 2pi ( 5R1) eo L

= net charge on the rod / 2pi ( 5 * 10^-9* 1* 10^-3) (8.85* 10^-12) 10* 10^-9

= net charge on the rod/2778.9 * 10^-33