EXAM 3 December 3, 1987 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. Magnetic transducers are often used to monitor small vibrations. For example, the end of a vibrating bar may be attached to an N-loop coil which in turn vibrates in and out of a uniform magnetic field B, as shown in the ___________ figure to the right. Show that |X X X | <---- the speed of the end of the bar, |X X X | dx/dt, is related to the EMF |___________| -----> induced in the coil by E = N B b dx/dt . 2. A straight wire of radius a placed along the axis of a cylindrical metal shell with inner radius b and outer radius c , carries a current I. The shell carries a current I in a direction opposite to that in the wire. Find the magnetic field B for a < r < b and also for r > c . Coaxial cables of this type are used widely to minimize unwanted magnetic effects. 3. (From homework) A resistor R and an inductor L are connected in parallel across an AC generator. The source EMF is E = E sin (omega t). Determine 0 the current through the resistor and the inductor (including amplitude and phase) as a function of time. What is the total current leaving the source (you need not make I algebraically tot pretty; any correct expression is acceptable). 4. So-called Helmholtz coils are sometimes used to obtain a uniform magnetic field in situations where a solenoid would be <----L----> impractical. Two coils of radius a, placed as shown in the figure to the O ---P--- O right, are used. Show that, if ^ coil of radius a L = a, then B at the point P has the value perpendicular to line 2 mu I a 0 2 2 -3/2 2 2 -3/2 B = --------- [ (a + x ) + (2a - 2ax + x ) ] 2