23.64 AGeiger counter detects radiation such as alpha particles by using the fac

Question

23.64 AGeiger 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 (Fig. P23.64). A large potential difference is established between the wire and the outer cylinder, with the wire at higher potential: this sets up a strong electric field directed radially out- ward. When ionizing radiation enters the device, it ionizes a few air molecules. The free electrons produced are accelerated by the elec- tric 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 to an audible "click." Suppose the radius of the central wire is 145 m and the radius of the hollow cylinder is 1.80 cm. What potential difference between the wire and the cylinder produces an electric field of 2.00 × 10" V/m at a distance of 1.20 cm frorn the axis of the wire? The wire and cylinder are both very long in comparison to their radii, so the results of Problem 2363 apply.) Figure P23.64 Radiation Free electron Counter

Explanation / Answer

As we know that

E = V/d

Distance between wire and cylinder is = 1.80 cm - 0.145 cm = 1.655 cm

As E = 2 x 104 V/m

Hence,

V = Ed = 2 x 104 x 0.01655 V

V = 331 Volts is the required potential difference between wire and cylinder.

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