Calculating Maximum Linear Charge Density in Geiger Tube

[doubled]

Homework Statement

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 0.450 mm and the inside diameter of the tube will be 4.20 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 5.55 106 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.


I'm not really interested in the answer, it's just the process I don't know how to do for this problem.

 

[doubled]

actually I found out how to do it, but can someone explain to me why we use the radius of the wire instead of cylinder to get our answer? What's the point of giving the radius of the cylinder then?

 

[Auxiliatricks]

XP I suppose I'm probably too late to be helpful now, but it's because the electrical field is strongest by the surface of the wire. If we used the radius of the cylinder, the electrical field everywhere else on the inside would be strong enough to cause an electrical discharge. The only point of it is to mislead I guess.