A Geiger counter detects radiation such as alpha particles by using the fact tha

Question

A Geiger counter detects radiation such as alpha particles by using the fact that the radiation ionizes the air along its path. A thin wire lies on the axis of a hollow metal cylinder and is insulated from it. A large potential difference is established between the wire and the outer cylinder, with the wire at a higher potential; this sets up a strong electric field directed radially outward. When ionizing radiation enters the device, it ionizes a few air molecules. The free electrons produced are accelerated by the electric field toward the wire and, on the way there, ionize many more air molecules. Thus a current pulse is produced that can be detected by appropriate electronic circuitry and converted into an audible click. Suppose the radius of the central wire is 145 micrometers and the radius of the hollow cylinder is 1.80 centimeters

Explanation / Answer

Electric field is proportional to 1/R in the long wire situation. ie E = x/R where x is a constant related to the volts at various points. at a distance of 0.012 m the electric field is 2.00 * 10^4 so x = ER = 2.00 * 10^4 * 0.012 = 240 The total volts is then the integral of x/R =240/R from the middle wire to the outer cylinder = 240 ln (R) from 145 * 10 ^ -6 to 0.018 m I calculate this to be about 1160 V

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