EXAM 1 March 8, 1988 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 -7 1/(4 pi epsilon ) = 9.0 x 10 N m / C mu /(4 pi) = 10 T m / A 0 0 -31 The mass of the electron is 9.11 x 10 kg. 1. (a). Describe a good way to reconstruct Coulomb's Law without memorization. You need not have a technique for finding the arbitrary form of the constant, and you may use anything in the heading of this exam. (b). Explain a good technique for determining without memorization how to determine the constant in Gauss's Law. You may assume that you know Coulomb's Law. [8 points each part] [The remaining problems count 28 points each.] 2. In the Bohr model of the hydrogen atom, an electron circles a proton at a radius of a . How fast must the electron 0 be moving if no forces other than the Coulomb attraction are large enough to matter? 3. (From homework) A thin cylindrical shell of radius R is 1 surrounded by a second concentric concentric cylindrical shell of radius R . The inner shell has a total charge +Q and the outer 2 shell -Q. (a) Assuming the length L of the shells is much greater than R or R , determine the electric field as a function 1 2 of r , the perpendicular distance from the common axis of the cylinders (the usual cylindrical-coordinate r) everywhere (i. e. inside both cylinders, between the two, and outside both). 4. A rod of length L is placed a distance b to the right of the origin. The charge density (Coul/m) on the rod is 2 2 3/2 lambda = -c ( x + a ) What is the electric field at the point x=0,y=a ? Note that a occurs in two different places in this problem.