Capacitance with a Geiger Tube

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SUMMARY

The discussion focuses on calculating the maximum potential difference and maximum charge per unit length in a Geiger tube, characterized by a central wire and a conducting cylindrical shell. The relevant equation for capacitance per unit length is C/L = 2πε / ln(a/b), where ε is the permittivity of the gas with a dielectric constant of 1.08. The maximum electric field (E) is determined by the dielectric strength of 1.00 x 10^6 V/m, which is essential for calculating the maximum charge. Participants provided guidance on deriving the necessary formulas and applying Gaussian surfaces for electric field calculations.

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  • Understanding of capacitance in cylindrical geometries
  • Familiarity with Gaussian surfaces and electric fields
  • Knowledge of dielectric materials and their properties
  • Ability to integrate functions related to electric fields
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  • Study the derivation of capacitance formulas for coaxial cylinders
  • Learn about electric field calculations using Gaussian surfaces
  • Research dielectric breakdown and its implications in capacitor design
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Physics students, electrical engineers, and anyone involved in the design or analysis of capacitors, particularly in applications involving Geiger tubes and cylindrical geometries.

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Homework Statement


The radius and the length of the central wire in a Geiger tube are 0.180 mm and 10.0 cm, respectively. The outer surface of the tube is a conducting cylindrical shell that has an inner radius of 1.50 cm. The shell is coaxial with the wire and has the same length (10.0 cm). The tube is filled with a gas that has a dielectric constant of 1.08 and a dielectric strength of 1.00*10^6 V/m.

(a) What is the maximum potential difference that can be maintained between the wire and shell?


(b) What is the maximum charge per unit length on the wire?



Homework Equations


C/L=2\pi\epsilon/lna/b

The Attempt at a Solution


I am completely befuddled by this. I'm not sure where to start even, I'd just like some one to please point me towards the start. I have no trouble working with single cylinders or with parallel plates but this is just beyond confusing to me. Advice? Thank you in advanced.

edit：whoa...that equation came out ugly...
0220.png
hopefully that works
 
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Yup, that's the right answer.
 
ideasrule said:
Yup, that's the right answer.

Sarcasm is not appreciated, I'm not asking for someone to do it for me...just some guidance.
 
I really wasn't trying to be sarcastic. You said:

1st2fall said:
edit：whoa...that equation came out ugly...
0220.png
hopefully that works

That IS the right answer for the capacitance. You couldn't have gotten that without answering at least part of (b) correctly, so I assumed you didn't need any more help. Now I know that you probably found that equation in the textbook and didn't derive it, but that wasn't clear from your first post.

For (b), if you take a cylindrical Gaussian surface surrounding the line of charge, you can calculate E. If the maximum E equals the dielectric breakdown value, that's when the charge held by the capacitor is the maximum possible.

For (a), you have to first derive a formula for potential difference. You already have an equation relating E and r from part (b), so integrate E*dr from a to b and you'll get the equation.
 

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