This formula is applicable for a point charge distribution.

In summary, a Geiger-Mueller tube is a particle detector used to detect ionizing radiation. It works by ionizing gas particles within a metal tube and amplifying the resulting electric current. The "E Field" is an important component that helps accelerate the charged particles for easier detection. The sensitivity of the tube is affected by its size, shape, and gas type/pressure. However, there are limitations to using a Geiger-Mueller tube, such as its inability to differentiate between types of radiation and limited detection range. To maintain accurate readings, the tubes must be regularly calibrated and maintained.
  • #1
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.

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]
 
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  • #2
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Paul Hurley said:

Homework Equations



V=(kq)/r

For what type of charge distribution is this formula applicable?
 

Related to This formula is applicable for a point charge distribution.

1. What is a Geiger-Mueller tube and how does it work?

A Geiger-Mueller tube is a type of particle detector used to detect ionizing radiation. It consists of a metal tube filled with a gas, usually a mixture of argon and methane. When ionizing radiation enters the tube, it ionizes the gas particles, creating an electric current. This current is amplified and can be measured to determine the level of radiation present.

2. What is the purpose of the "E Field" in a Geiger-Mueller tube?

The "E Field," or electric field, is a crucial component of a Geiger-Mueller tube. It is created by applying a high voltage to the tube, which helps to accelerate the charged particles produced by ionizing radiation. This increased acceleration results in a higher current and makes it easier to detect and measure the radiation.

3. How does the design of a Geiger-Mueller tube affect its sensitivity?

The sensitivity of a Geiger-Mueller tube is affected by its size and shape. A larger tube will have a larger volume of gas, making it more sensitive to radiation. The shape of the tube also plays a role, as a thinner tube will have a higher electric field, resulting in increased sensitivity. Additionally, the type and pressure of gas used in the tube can also impact its sensitivity.

4. What are the limitations of using a Geiger-Mueller tube for radiation detection?

While Geiger-Mueller tubes are commonly used for detecting radiation, they do have some limitations. They are only able to detect ionizing radiation and are not able to differentiate between different types of radiation. Additionally, they have a limited range of detection and can become saturated at high levels of radiation, making them less accurate.

5. How are Geiger-Mueller tubes calibrated and maintained for accurate readings?

To ensure accurate readings, Geiger-Mueller tubes need to be calibrated and maintained regularly. This involves comparing the readings from the tube to a known source of radiation and adjusting the voltage or other parameters as needed. The tubes also need to be checked and cleaned to ensure that they are free from any obstructions that could affect their sensitivity.

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