Chapter 30, Problem 86EAP

High-frequency signals are often transmitted along a coaxial cable, such as the one shown in FIGURE CP3O.86. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius $r_1$while the outer conductor of radius $r_2$is grounded. A soft, flexible insulating material fills the space between them, and an insulating plastic coating goes around the outside.

a. Find an expression for the inductance per meter of a coaxial cable. To do so, consider the flux through a rectangle of length l that spans the gap between the inner and outer conductors.

b. Evaluate the inductance per meter of a cable having $r_1=0.50\text{mm}$ and $r_2=3.0\text{mm}$ .