A Geiger-Mueller tube is a radiation detector that consists of a closed, hol- low, metal cylinder (the cathode) of inner radius r, and a coaxial cylindri- cal wire (the anode) of radius r, (Fig. P24.42a). The charge per unit length on the anode is A, and the charge per unit length on the cathode is -A. A gas fills the space between the electrodes. When the tube is in use (for example, in measuring radioactivity from fruit in Fig. P24.42b) and a high-energy elementary particle passes through this space, it can ionize an atom of the gas. The strong electric field makes the resulting ion and electron accelerate in opposite directions. They strike other mole- cules of the gas to ionize them, producing an avalanche of electrical discharge. The pulse of electric current between the wire and the cylinder is counted by an external circuit. (a) Show that the magnitude of the electric potential differ- ence between the wire and the cylinder is AV= 2k Aln (b) Show that the magnitude of the electric field in the space between cathode and anode is AV E = In (r. /r.) (7) where r is the distance from the axis of the anode to the point where the field is to be calculated. Cathode Anode a Figure P24.42 wellphoto/Shutterstock

A Geiger-Mueller tube is a radiation detector that consists of a closed, hol- low, metal cylinder (the cathode) of inner radius r, and a coaxial cylindri- cal wire (the anode) of radius r, (Fig. P24.42a). The charge per unit length on the anode is A, and the charge per unit length on the cathode is -A. A gas fills the space between the electrodes. When the tube is in use (for example, in measuring radioactivity from fruit in Fig. P24.42b) and a high-energy elementary particle passes through this space, it can ionize an atom of the gas. The strong electric field makes the resulting ion and electron accelerate in opposite directions. They strike other mole- cules of the gas to ionize them, producing an avalanche of electrical discharge. The pulse of electric current between the wire and the cylinder is counted by an external circuit. (a) Show that the magnitude of the electric potential differ- ence between the wire and the cylinder is AV= 2k Aln (b) Show that the magnitude of the electric field in the space between cathode and anode is AV E = In (r. /r.) (7) where r is the distance from the axis of the anode to the point where the field is to be calculated. Cathode Anode a Figure P24.42 wellphoto/Shutterstock

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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