High-frequency signals are often transmitted along a coaxial cable, such as the one shown in FIGURE P26.66. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius R₁ while the outer conductor of radius R₂ is grounded (i.e., at V = 0 V). An insulating material fills the space between them, and an insulating plastic coating goes round the outside.

a. Find an expression for the capacitance per meter of a coaxial cable. Assume that the insulating material between the cylinders is air.
b. Evaluate the capacitance per meter of a cable having R₁ = 0.50 mm and R₂ = 3.0 mm.