Paul Hurley
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1. The problem: A Geiger-Mueller tube is part of a Geiger counter, a device used to count the number of ionizing particles passing through it. It consists of a conducting outer cylinder held at zero electric potential with a thin central wire held at an electric potential of roughly 1000 volts. The dimensions of the device are: inner wire diameter 25 microns, tube diameter 2.5 cm, length 10 cm. Although the tube is finite, you may model the electric fields as those due to an infinite cylinder.
(a) Calculate the electric field strength at the surface of the wire and the inside surface of the tube.
(b) Is the electric field strength at the wire above dielectric breakdown for dry air (3 MV/m)? The answer is yes… at what distance from the wire would is the critical value exceeded? The gas in the Geiger tube is an inert gas held at such a pressure that spontaneous breakdown does not occur.
E.dA=q/epsilon naught
V=(kq)/r[/B]
For the surface of the wire:
V = (kq)/r = 1000v
q = 1000r/k
E.dA = q/epsilon naught
E(pi*r^2*L) = (1000r)/(k*epsilon)
E = 1000/(k*epsilon*pi*(1.25e^-5m)*(.1m))
E = .32 N/C
This however is not even close to 3 MV/m, so what am I doing wrong?
I also don't understand the other two parts of this question since I can't figure out the first.
Thank you anyone for help in advance!
[/B]
(a) Calculate the electric field strength at the surface of the wire and the inside surface of the tube.
(b) Is the electric field strength at the wire above dielectric breakdown for dry air (3 MV/m)? The answer is yes… at what distance from the wire would is the critical value exceeded? The gas in the Geiger tube is an inert gas held at such a pressure that spontaneous breakdown does not occur.
Homework Equations
E.dA=q/epsilon naught
V=(kq)/r[/B]
The Attempt at a Solution
For the surface of the wire:
V = (kq)/r = 1000v
q = 1000r/k
E.dA = q/epsilon naught
E(pi*r^2*L) = (1000r)/(k*epsilon)
E = 1000/(k*epsilon*pi*(1.25e^-5m)*(.1m))
E = .32 N/C
This however is not even close to 3 MV/m, so what am I doing wrong?
I also don't understand the other two parts of this question since I can't figure out the first.
Thank you anyone for help in advance!
[/B]