- B Consider An Infinitely Long Straight Cylindrical Rod Of Conducting Material In An Inertial Cartesian Frame S X Y 1 (61.45 KiB) Viewed 26 times
(b) Consider an infinitely long, straight, cylindrical rod of conducting material in an inertial Cartesian frame S'(x,y', z', t'), where it has radius a and is stationary. In this frame, the rod is symmetric about the z' axis. Free current flows inside the solid rod in a direction parallel to z' axis. Current density in this frame varies as a function of cylindrical radial distance R', according to: J{(R') = K. exp(-(R')?/14), where Ko and I are positive constants. The rod is electrically neutral - that is, its total macroscopic charge density is zero (negative and positive charges balance in the material). The medium outside the rod is vacuum. In another inertial frame S(x,y,z, t), whose axes coincide with those of S' at time t = t' = 0, the rod appears to be moving with velocity v in the x direction. (1) Show that the cross section of the rod (a circle of radius a in S') appears elliptical in frame S, described by a curve parallel to the xy plane which satisfies (x - x)2 ya = 1. (Evaluate the parameter x, and the constants C, and c, as part of your answer). (ii) Give a physical explanation for why the current density at any given point, as viewed in frame S, will have the same value as that in frame s', even though the cross section of the rod appears different in the two frames. +