A long, straight wire has length L and a circular cross section with area a 2 .

A long, straight wire has length L and a circular cross section with area πa². Arrange two such wires so they are parallel and separated by a distance d. You may assume that L >> d >> a and ignore end effects.

(a) Graph the electrostatic potential along the straight line which connects the center of one wire to the center of the other wire for the case when the two wires have equal and opposite charge per unit length.
(b) Derive an approximate expression for the capacitance of this two-conductor system.