The radius and the length of the central wire in a Geiger tube are 0.19 mm and 1
ID: 2135606 • Letter: T
Question
The radius and the length of the central wire in a Geiger tube are 0.19 mm and 11 cm, respectively. The outer surface of the tube is a conducting cylindrical shell that has an inner radius of 1.5 cm. The shell is coaxial with the wire and has the same length (11 cm). The tube is filled with a gas that has a dielectric constant of 1.08 and a dielectric strength of 2 x 106 V/m.
1)What is the maximum potential difference that can be maintained between the wire and shell?
2)What is the maximum charge per unit length on the wire?
Explanation / Answer
a)
r= 0.19 mm =0.19*10^-3 m
R=1.5 cm
K=1/4pieo =1/4p*(8.85*10^-12) =9*10^9
k =dielectric constant =1.08
lambda =charge per unit length
Electric field E is
E=2K*almbda/kr
=>(2K*lambda/k)=Er =2*10^6*0.19*10^-3 =380
R=0.11 m
Vmax=(2Klamba/k)ln(R/r)
Vmax =380*ln(1.5/0.19*10^-3)
Vmax =2535 V or 2.535 KV
b)
lambda =Q/L =Ekr/2K =(2*10^6)*1.08*0.19*10^-3/(2*9*10^9)
lambda =2.28*10^-8 C/m or 22.8 nC/m
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