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The Geiger-Mueller tube is a radiation detector consistingessentially of a closed, hollow metal cylinder, called the cathode,of inner radius ra, and a coaxial cylindrical conductor,called the anode, the anode of radius The linear charge density ofthe anode of 𝜌𝐿 , and the linear charge density of the cathode is−𝜌𝐿 . A gas fills the space between the electrodes. When ahigh-energy elementary particle passes through such a gap, it canionize a gas atom. The strong electric field causes the resultingion and electron to accelerate in opposite directions. As theymove, they collide with other gas molecules and ionize them,producing a chain of electrical discharge. The energy flow betweenthe conductor and the cylinder is measured by an externalcircuit.
A. Determine that the potential difference between theconductor and the cylinder is:
B. Imagine that the inside diameter of the Geiger-Muellertube described above is 2.50 cm and that the conductor on its shafthas a diameter of 0.200 mm. The breakdown field of the gascontained between the central conductor and the cylinder is1.2x10^6 V/m. Use the results of the previous situation tocalculate the maximum voltage that can be applied between theconductor and the cylinder before dielectric breakdown occurs inthe gas.
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