In preparation for an experiment that you will do in your introductory nuclear p

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 X 10^-4 m and 1.2 X 10^-1 m, respectively. The outer surface of the tube is a conducting cylindrical shell that has an inner radius of 1.5 X 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)
given

a = 2*10^-4 m

b = 1.5*10^-2 m

L = 0.12 m

Capacitnace of cyllinrical capcacitor, C = 2*pi*epsilon*L/ln(b/a)

= 2*pi*8.854*10^-12*0.12/ln( 1.5*10^-2/(2*10^-4))

= 1.55*10^-12 F

b) Total charge on capacitor, Q = C*V

= 1.55*10^-12*1200

= 1.85*10^-9 C

linear charge density on the wire = Q/L

= 1.85*10^-9/0.12

= 1.54*10^-8 C/m

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