- 4 An Infinitely Long Cylinder Of Radius R Carries Fixed Charges The Charge Density At T 0 Given In Cylindrical Coor 1 (132.26 KiB) Viewed 27 times
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4. An infinitely long cylinder of radius R carries fixed charges. The charge density at t = 0, given in cylindrical coordinates, is P(r) = Doe-z2/a2 - where a is a constant with units of length and po has units of charge per volume. The cylinder is dragged with speed v long its axis. a) Sketch a plot of the charge density as a function of z at t= 0. At which value of z is the density greatest? b) Sketch a plot of the charge density as a function of z at t= 1. At which value of z is the density greatest? c) Show that the density at any later time is = p(r,t) = poe-(z–vt)2/a d) Determine an expression for the current density at any time and show that it satisfies the continuity equation.