Voltage Limit on an Ionization Chamber

## Question:

A cylindrical ionization chamber has a central wire anode of radius 0.20 mm, and a coaxial cylindrical cathode of radius 10 mm. It is filled with a gas whose dielectric strength is 2.2 M Vm^-1. What is the largest p.d. that should be applied between anode and cathode if the gas is not to suffer electric breakdown before radiation penetrates the mica window?

An ionization chamber is a type of radiation detector. It is filled with a dielectric gas and charged by a potential difference between conductors. The electrons in the gas atoms are bound to their nucleii by electric forces. If an electron is given enough energy to exceed the ionization potential of the atoms, an electron will be torn away from the atom and accelerated by the electric field in the chamber. It may then bang into the electrons of other atoms, giving them enough energy to become free, causing a cascade of electrons to be collected on the postively charged electrode of the chamber.

The energy required to start an electron cascade may come from the applied electric field if it is too large. Ideally the applied field will be close to but not quite enough to trigger a discharge in the ionization chamber. Then when an external source of energy comes along, like a gamma ray for example, it will add enough energy to set off the cascade and cause a pulse of current through the ionization chamber. In this way the incoming gamma ray may be detected.

Your question comes down to calculating the maximum electric field for the ionization chamber geometry given in the problem, as a function of the applied potential difference. Then setting that field function equal to the given dielectric strength of the gas filling the tube. Solving that equation for the potential difference will give you an answer.

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