A certain transmission line is constructed from two thin metal “ribbons,” of width w, a...

A certain transmission line is constructed from two thin metal “ribbons,” of width w, a very small distance apart. The current travels down one strip and back along the other. In each case, it spreads out uniformly over the surface of the ribbon.

(a) Find the capacitance per unit length, C.

(b) Find the inductance per unit length, L.

(c) What is the product LC, numerically? [L and C will, of course, vary from one kind of transmission line to another, but their product is a universal constant— check, for example, the cable in Ex. 7.13—provided the space between the conductors is a vacuum. In the theory of transmission lines, this product is related to the speed with which a pulse propagates down the line:

(d) If the strips are insulated from one another by a nonconducting material of permittivity ? and permeability μ, what then is the product LC?What is the propagation speed? [Hint: see Ex. 4.6; by what factor does L change when an inductor is immersed in linear material of permeability μ?]