# 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 Îµ. Show that when D is large compared to r, the capacitance of the pair of conductors per unit length is given approximately by,
Solution
We consider a line charge distribution of density Î» 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.
Capacitance between two wire transmission lines

The electric field intensity at the point P is due to both the charges and is written as,

The potential at P is given as,

Hence, the capacitance of the pair of conductors per unit length is given as,