PHS 212 Final, Spring 2005

NDU PHS 212 - Electricity & Magnetism Faculty of Natural and Applied Sciences Final Exam - Spring 2005 Department of Sciences Duration: 120 minutes (2h) 1. In a mass Spectrometer, an ion of charge +Ze and mass M enters a region of unifomn field B, and travels in a semi-circle until it hits a the wall a distance d from where it entered (see the z ’ figure). If the ion achieved its energy by being accelerated through a ‘voltage difference V, Baz - : d sy By show that M= =} es) 3 F & Qa $. g > a & & o G s by cg e a 8 g Ca Q oe a m & a 2 6 & 5 Ag Me | | [Sher B R 1 : 0 v, 1. . « _* L | Yay T (at yb ; at mw Vy =?2y AV. the electric field at this point. . Consider a co-axial cable with inner current 2/ into the page ‘and uniformly. distributed over r < a,and outer current J out the page and uniformly distributed over b < r < c. Find the magnetic field (magnitude and direction) for a) r < a, b) a<r<b,c)b<r<c,andd)r>c. . You are given three initially uncharged conducting spheres of radii 5, cm, 15 cm and 30 cm. They are placed at large distances from each other. The 15-cm sphere is- Fhen- -charged to a potential of 1000 V. Once isolated it is connected by a thin wire to the 5-cm sphere. (a) Find the potentials and charges of the 15-cm and 5-cm spheres once equilibrium is reached. _ (b) The thin wire is now disconnected. The 15-cm sphere is then connected to the still uncharged 45- cm sphere. Find the potentials and charges of the two spheres once equilibrium is reached. (c) The thin wire is disconnected. We now proceed to connect the 5-cm sphere to the }5-cm sphere with a thin wire. Find the potentials and charges of the two spheres once equilibrium is reached.