In Young & Freedman An annulus with an inner radius of a and an outer radius of b has charge density o and lies in the xy-plane with its center at the origin (see the figure). (a) Using the convention that the potential vanishes at infinity, determine the potential at all points on the z-axis. (b) Determine the electric field at all points on the z-axis by differentiating the potential. (c) show that in the limit a + 0,6 â€" 09, the electric field reproduces the result for an infinite plane sheet of charge. (d) If a = 5. 00 cm, b = 10. 0 cm and the total charge on the annulus is 1. 00 4C, what is the potential at the origin? (e) If a particle with mass 1. 00 g (much less than the mass of the annulus) and charge 1. 00 uC is placed at the origin and given the slightest nudge, it will be projected along the z-axis. In this case, what will be its ultimate speed?
