EXAM 2 April 12, 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 ) = 9.1 x 10 N m / C 0 -7 mu / (4 pi) = 10 T m/ A 0 -31 The mass of the electron is 9.11 x 10 kg. 1. (a). Explain the relationships among Force, Electric Field, Potential Energy, and Electrical Potential. How can you use these relationships to remember the formula giving the Electrical Potential when the Electric Field is known? (b). What are the relationships among the formulae for effective capacitance for series and parallel combinations of capacitors and the effective resistance for series and parallel combinations of resistors? 2. (Simplified from homework). Determine the current through each of the resistors in the figure below. Write down the junction and both possible loop equations explicitly. [Hint: with a little thought, you can do the algebra for this problem rather easily.] _______ R ________________ R _____ | 2 | 2 | __|__ | __|__ _________ V r __________ V | | | | | | r ______|_______ r | _____ 2V | | | | |_______ R _______|_________ R ______| 1 1 [Don't miss the r 's in the vertical branches] 3. A spherical capacitor is to be constructed by using a metal sphere of radius b as one plate and a concentric spherical metal shell of inner radius a as the other plate. (a). Use Gauss's law to determine the electric field between the plates. (b). How is the result for this field changed if a dielectric of dielectric constant epsilon completely fills the volume between the plates? (c). Find the capacitance of the device when the dielectric is present (or in the absence of dielectric if you cannot complete part (b) ). 4. A coil of wire is wound on an evacuated, hollow glass tube with inner diameter d meters. The coil produces a uniform magnetic field of B parallel to the axis of the tube. Protons with speed v are shot into the tube at a point on its axis. What is the maximum angle to the axis that a particle can be moving as it enters the tube if it is not to hit the wall as it spirals down the tube?