The figure is a section of a conducting rod of radius R1 = 1.40 mm and length L
ID: 1419657 • Letter: T
Question
The figure is a section of a conducting rod of radius R1 = 1.40 mm and length L = 13.90 m inside a thin-walled coaxial conducting cylindrical shell of radius R2 = 12.9R1 and the (same) length L. The net charge on the rod is Q1 = +3.70 × 10-12 C; that on the shell is Q2 = -2.13Q1. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.30R2? What are (c) E and (d) the direction at r = 5.11R1? What is the charge on the (e) interior and (f) exterior surface of the shell?
Explanation / Answer
a)Length is very large compared to radius, we can assume it infinite wire.
E = 2k lambda/r =2*9e9*(1-2.13)(Q/L)/[2.3R2]
= -18e9*1.13*(3.7e-12/13.9)/[2.3*12.9*0.0014] outward
= 0.1303 N/C inward
b) inward
c) when r = 5.11R1, it will be inside cylinderical shell, so cylinder will not contribute to electric field
E = 2*9e9*(1)(Q/L)/[5.11R1]
= 18e9*1*(3.7e-12/13.9)/[5.11*0.0014] outward
= 0.670 N/C ouward
d) outward
e) interior surface = -Q1 = -3.70 × 10^-12 C
f) exterior surface charge = Q2- interior surface = -2.13Q1 + Q1 = -1.13Q1 = -1.13*3.7e-12
= -4.18 * 10^-12 C