EXAM 2 April 15, 1992 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. (10 points) (a) Give a good argument for remembering the following: (1). The electric potential caused by a point charge. (2). The capacitance of a parallel plate capacitor. (3). The resistance of a wire of given resistivity and size. (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. Derive with reasonable care the expression for the capacitance of a parallel-plate capacitor, whose plates are a constant distance d from each other, and each of which has the same shape and a total area of A . Assume d << the length and width of the plates. The management suggests getting the same result as that in problem 1a. Some extra credit will be given for accurately including the effects of a dielectric between the plates. 3. (Simplified from homework) Determine the current through each of the resistors in the figure below, where R = R and 4 2 R = R . Show all the equations that would be necessary to solve the 3 1 problem if the resistors were not related, and then use symmetries to simplify and solve the problem. _______ R ________________ R _____ | 4 | 2 | __|__ | __|__ _________ V R __________ V | 5 | | | | |_______ R _______|_________ R ______| 3 1 4. A flat disk of radius b carries a constant surface 2 charge density of sigma [in C/m ] and rotates around an axis AA' perpendicular to the disk and passing through its center. It rotates at an angular speed of omega [in 1/sec]. Show that each ring of width dr carries a current dI = sigma * omega * r * dr [It may help to think of the surface charge density as sigma = rho*h , where rho is a volume charge density and h is the thickness of the charge layer]. Given this expression for -> the current, and a constant magnetic field B perpendicular to the axis of rotation, show that the torque on the disk is 1 4 tau = - * sigma * omega * pi * B * b 4