Question

An infinitely long, thin wire contains a uniform charge density +λo and is oriented along the z-axis. Assume that the potential at s = 0 is zero. a) Find an expression for the electric field for the wire in Cartesian coordinates and convert it to cylindrical coordinates. b) Use your answer from (a) to solve for an expression for the electric potential at a distance s from the wire. Use cylindrical coordinates for this. c) Now solve for an expression for the electric potential for the same wire, only now it is located at x = a. d) Use your solution to (c) to solve for the potential due to TWO wires, one with charge density +λo located at x = a and one with charge density −λo located at x = −a. e) Use your solution to (d) to solve for the electric field due to these two wires. Confirm that this matches the result you would have found if you had just modified your answer from (a). Note: Electric fields/forces add in superposition. The reason I am asking you to go through all these steps is to show that electric potentials ALSO add in superposition. It may be helpful to keep that in mind while working on this problem.

Answer 1