<p>A detector of radiation called a Geiger tube consists of a closed, hollow, co

Question

<p>A detector of radiation called a Geiger tube consists of a closed, hollow, conducting cylinder with a fine wire along its axis. Suppose that the internal diameter of the cylinder is <span>2.00</span> cm and that the wire along the axis has a diameter of 0.200 mm. The dielectric strength of the gas between the central wire and the cylinder is <span>1.10</span> <img title="multiplied by" src="http://www.webassign.net/images/multiply.gif" alt="multiplied by" /> <span>10⁶</span> V/m. Calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas</p>

Explanation / Answer

Given data Internal radius of the cylinder is, R = 1.0 cm                                                           = (1.0 cm) (0.01 m /1 cm)                                                           = 0.01 m Radius of the wire is, r = (0.2 mm) /2                                       = (0.1 mm) (0.001 m / 1mm )                                       = 1.0 *10-4 m The dielectric strength of the gas is, E = 1.10 * 106 V/m Let the maximum potential difference be V Solution: The maximum potential difference can be calculated by using the relation between electric field and potential difference, that is,                          E = [ V / ln (R / r ) ] (1/ r)   1.10 * 106 V/m = [ V / ln (0.01 m / 1.0 *10-4 m )] (1/1.0 *10-4 m)                              = (V /4.605) (1.0 *10+4 m )                        V = 506.55 V

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