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Solved Problem-5

Problem-5
A transmission line consists of a pair of long parallel conductors of radius r with a spacing D between centres in a medium of permittivity ε. Show that when D is large compared to r, the capacitance of the pair of conductors per unit length is given approximately by,
Description: 168968.png
Solution
We consider a line charge distribution of density λ between the two cylindrical conductors. If the charge on the conductor A is positive, it will be negative on the conductor B by electrostatic induction.
Description: 168959.png
Capacitance between two wire transmission lines
 
The electric field intensity at the point P is due to both the charges and is written as,
Description: 168952.png
 
The potential at P is given as,
Description: 168943.png
 
Hence, the capacitance of the pair of conductors per unit length is given as,
 
Description: 168936.png
 
Description: 168927.png
 





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