For your senior project you are designing a Geiger tube for

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 0.500 mm and the inside diameter of the tube will be 4.00 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 5.50 Times 10^6 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.

Solution

the linear charge density is calculated as follows:

    lambda = 2*pi*e₀RE_max

                = 2*pi*8.854x10^-12*0.25x10^-3*5.5x10⁶

                = 76.5x10^-9 C/m

                = 76.5 nC/m