Two long, straight copper pipes, each of radius R, are held a distance 2d apart. One is...

Two long, straight copper pipes, each of radius R, are held a distance 2d apart. One is at potential V₀, the other at −V₀ (Fig. 3.16). Find the potential everywhere. [Hint: Exploit the result of Prob. 2.52.]

Reference figure 3.16

Reference Prob. 2.52

Two infinitely long wires running parallel to the x axis carry uniform charge densities +λ and −λ (Fig. 2.54).

(a) Find the potential at any point (x, y, z), using the origin as your reference.

(b) Show that the equipotential surfaces are circular cylinders, and locate the axis and radius of the cylinder corresponding to a given potential V₀.