EXAM 3 May 5, 1989 PS 208 If you need a constant not given here or do not understand a problem, please ask me about it. No notes, books, etc. may be used during this exam. 2 -19 g = 9.8 m/sec e = 1.6 x 10 C 9 2 2 1/ (4 pi epsilon ) = 9.0 x 10 N m / C 0 -31 The mass of the electron is 9.11 x 10 kg. 1. (10 points). (a) Give a good, quick way of remembering the Biot-Savart law for the magnetic field due to a infinitesimal segment of current. (b) Name the magnetic-field equivalent of Gauss's Law for electric fields and explain the analogies between the two. 2. (From homework) (a). Find a ______________________ | | | differential equation for the current | | R V R 2 0 1 | through the inductor in the circuit | | L | | | |__________|__________| shown to the right. No other current should appear in the equation. (b). at Show that I = A + B e satisfies the differential equation. Determine all constants so that the current is known for all times. 3. A metal bar slides down an inclined plane in contact with two wires along the edges of the plane. The wires are connected together at the bottom of the plane, and they are a distance b apart. If the bar slides from rest down the incline, and a magnetic field B is directed vertically upward, find an equation for the induced EMF between the ends of the sliding rod as a function of time. Assume negligible friction and large resistance in the bar. Show the direction of the (negligibly small) current that flows in the circuit. 4. A very long, straight metal tube has inner radius a and outer radius b . A current whose density is J = cr flows down the tube. Find the magnetic field in the empty region inside r = a and also within the metal, a < r < b .