The figure represents a transmission line consisting of two, parallel perfect conductors of arbitrary, but constant, cross section. Current flows down one conductor and returns via the other.
Show that the product of the inductance per unit length L and the capacitance per unit length C is
LC=μϵ
where μ and ϵ are the permeability and the permittivity of the medium surrounding the conductors. (See the discussion about magnetic fields near perfect conductors at the beginning of Section 5.13.)