EXAM 1 October 7, 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. Two point charges Q and Q are a distance d apart, 1 2 and their combined charge is Q . If they repel each other tot with a force F, find the two charges in terms of Q , d , and tot F. 2. A force F = + kx acts on a particle of mass m. (a) Show that the differential equation governing the motion of 2 d x the particle is m --- - kx = 0 . 2 dt alpha t (b) Show that e is a solution of this equation and find the appropriate value or values of alpha . (c) Interpret the solution physically (i. e. by describing it qualitatively or by sketching it). What is wrong with this motion, and where does the problem arise? 3. (From homework). A thin cylindrical shell of radius R is 1 surrounded by a second concentric cylindrical shell of radius R . The inner shell has a total charge of - Q and the outer 2 1 shell + Q , with Q > Q > 0 . Assuming the length L of the shells 2 2 1 is much greater than either radius, determine the electric field as a function of r (the perpendicular distance from the common axis of the cylinders) for all values of r . 4. A long thin rod is bent into the form of a semicircle of radius b , with its ends on the x axis at x=+b and x=-b. The rod carries a charge density lambda = A cos (theta), where A is a constant and the angle theta is measured from the right end. Find the y-component of the electric field at the origin (the center of the circle).