The figure is a section of a conducting rod of radius R_1 = 1.50 mm and length L
ID: 1546018 • Letter: T
Question
The figure is a section of a conducting rod of radius R_1 = 1.50 mm and length L = 13.20 m inside a thin-walled coaxial conducting cylindrical shell of radius R_2 = 10.7R_1 and the (same) length L. The net charge on the rod is Q_1 = +3.53 times 10^12 C; that on the shell is Q_2 What arc the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r - 2.25R_2? What are (c) E and (d) the direction at r = 5.01 R_1? What is the charge on the (e) interior (f) exterior surface of the shell?Explanation / Answer
from the Gauss law
E ( 2pi rL) =q_enclo/ eo
E = q_encl/ 2pi eo rL
q_encl= Q1 + Q2 = 3.53 * 10^-12 + ( -2.25 ( 3.53 * 10^-12 )
=-4.4125 * 10^-12 C
E = 1/ 2pi ( 8.85 * 10^-12 ) * (- 4.4125 * 10^-12 C)/16.05 * 10^-3 m ( 13.20)
=-0.374 N/C
magnitude 0.374 N/C
(b)
radially inward due to q_enclose < 0
(c)
r= 2.25 R2 = 2.25 ( 16.05 * 10^-3 m) = 36.1125 * 10^-3 m
E = 1/ 2pi ( 8.85 * 10^-12 ) * ( 3.53 * 10^-12 C)/36.1125 * 10^-3 m ( 13.20)
=0.133 N/C
(d)
radially outward due to q_enclose > 0