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Capacitance with a Geiger Tube

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data
    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?



    2. Relevant equations
    C/L=2[tex]\pi\epsilon[/tex]/ln[tex]a/b[/tex]

    3. 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
     
  2. jcsd
  3. Feb 25, 2010 #2

    ideasrule

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    Homework Helper

    Yup, that's the right answer.
     
  4. Feb 25, 2010 #3
    Sarcasm is not appreciated, I'm not asking for someone to do it for me....just some guidance.
     
  5. Feb 25, 2010 #4

    ideasrule

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    I really wasn't trying to be sarcastic. You said:

    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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