In preparation for an experiment that you will do in your introductory nuclear p
ID: 2180451 • Letter: I
Question
In preparation for an experiment that you will do in your introductory nuclear physics lab, you are shown the inside of a Geiger tube. You measure the radius and the length of the central wire of the Geiger tube to be 2.0 10-4 m and 1.2 10-1 m, respectively. The outer surface of the tube is a conducting cylindrical shell that has an inner radius of 1.5 10-2 m. The shell is coaxial with the wire and has the same length (0.12 m).(a) Calculate the capacitance of your tube, assuming that the gas in the tube has a dielectric constant of 1.00.
_____ F
(b) Calculate the value of the linear charge density on the wire when the potential difference between the wire and shell is of 1.20 kV.
_____ C/m
Explanation / Answer
a)
C = 2 pi L e0/Ln(b/a) = 2*3.1416*0.12*8.85e-12/(Ln(1.5e-2/2e-4)) = 1.5455e-12
C = 1.55 * 10^-12 F
b)
Q = CV = 1.5455e-12 * 1.2e3 = 1.8546 * 10^-9 C
sigma = Q/2piaL = 1.8546e-9/(0.12) = 1.55 * 10^-8 C/m