THE FIELDS OF MOVING CHARGES — Edward Purcell & David Morin
Physics — E&M · tapered-rod
Problem
Tapered rod *
Two graphite rods are of equal length. One is a cylinder of radius a. The other is conical, tapering (or widening) linearly from radius a at one end to radius b at the other. Show that the end-to-end electrical resistance of the conical rod is a/b times that of the cylindrical rod. Hint: Consider the rod to be made up of thin, disk-like slices, all in series. (This result is actually only an approximate one, valid in the limit where the taper is slow. See Problem 4.6 for a discussion of this.)