For your senior project, you are designing a Geiger tube fordetecting radiation
ID: 1682494 • Letter: F
Question
For your senior project, you are designing a Geiger tube fordetecting radiation in the nuclear physics laboratory. Thisinstrument will consist of a long metal cylindrical tube that has along straight metal wire running down its central axis. Thediameter of the wire will be 0.515 mm andthe inside diameter of the tube will be 3.96 cm. The tube is to be filled with a dilute gas inwhich an electrical discharge (breakdown of the gas) occurs whenthe electric field reaches 5.15 X106 N/C. Determine the maximum linearcharge density on the wire if breakdown of the gas is not tohappen. Assume that the tube and the wire are infinitelylong._____________ nC/m
I am particularly confused about how to use the two diameters givenplease help :)
For your senior project, you are designing a Geiger tube fordetecting radiation in the nuclear physics laboratory. Thisinstrument will consist of a long metal cylindrical tube that has along straight metal wire running down its central axis. Thediameter of the wire will be 0.515 mm andthe inside diameter of the tube will be 3.96 cm. The tube is to be filled with a dilute gas inwhich an electrical discharge (breakdown of the gas) occurs whenthe electric field reaches 5.15 X106 N/C. Determine the maximum linearcharge density on the wire if breakdown of the gas is not tohappen. Assume that the tube and the wire are infinitelylong.
_____________ nC/m
I am particularly confused about how to use the two diameters givenplease help :)
Explanation / Answer
In this problem we really are just concerned with the charge on thewire. Since we are only concerned with the field inside ifthe outer cylinder then we won't need to worry about the fieldgenerated from the cylinder. Recall that when inside acylindrical shell the charge is 0, therefore it won't produce inelectric field if we are inside the cylinder. To find thelinear charge density on the wire we take use Gauss' Law and make acylindrical gauss surface that encloses the wire. The surfaceshould be a cylinder with the same radius as the wire and it'scenter should be placed at the center of the wire. Then weuse Gauss' Law and plug in some numbers to come up with ouranswer. Below are the equations that I used to solve theproblem. If we let E = electric field and = linear charge densitythen: Flux = (L)/ We can rewrite this as E(2*r*L) = (L)/ Then solving for the linear charge density we get=*E*2*r and from here we can just plug innumbers... =(8.85*10-12)*(5.15*106)*(2)*(.000515)/2= 7.37*10-8 C/m Then divide by 10-9 to put the units in nC:7.37*10-8/10-9 = 73.70 nC/m
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