Consider two thin, ideal, conducting wires of radius a centered on r? = (?d/2,0,0) and r+ = (d/2, 0, 0), parallel to the z axis and extending to infinity. Assume that both conductors are in a vacuum.
compute the capacitance per unit length of the two wires on the assumption that the radii of the conductors is much less than their separation d and that there is a linear charge density ? on the conductor centered on r? = (?d/2, 0, 0) and a linear charge density? on the conductor centered on r+ = (d/2,0,0). Hints: Compute the electric field in the region between the two conductors seperately and then use the principle of superposition to get the total electric field between the wires. Then integrate the electric field along a path from one conductor to the other to get the potential difference. If you’ve done everything correctly, your answer will involve the logarithm of the ratio d/a. Remember d ? a. Now use the definition of capcitance in terms of charge and voltage to compute the capacitance per unit length.