For your senior project, you are designing a Geiger tube for detecting radiation

Question

For your senior project, you are designing a Geiger tube for detecting radiation in the nuclear physics laboratory. This instrument will consist of a long metal cylindrical tube that has a long straight metal wire running down its central axis. The diameter of the wire will be 0.520 mm and the inside diameter of the tube will be 4.16 cm. The tube is to be filled with a dilute gas in which an electrical discharge (breakdown of the gas) occurs when the electric field reaches 5.35x10^6 N/C. Determine the maximum linear charge density on the wire if breakdown of the gas is not to happen. Assume that the tube and the wire are infinitely long.

Explanation / Answer

The electric field due to a long straight conductor fro the centre along the line parellel to the axis of the wire is given by E = (lambda)/2(pi)e0r Where lambda is the linear charge density of the wire e0 is the permiability of free space = 8.85*10^-12 Nm^2/C^2 r is the distance of the point from the centre of the wire Here r is the inner radius of the cylender = 4.16 cm/2 = 2.08*10^-2 m 5.35x10^6 N/C = (lambda)/2*(3.14)*(8.85*10^-12 C^2/Nm^2)*2.08*10^-2 m lambda = 6.18*10^-6 C/m

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