EXAM 1 March 13, 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 = 9.0 x 10 N m / C 0 -31 The mass of the electron is 9.11 x 10 kg. 1. [10 points] Describe a good way to reconstruct Gauss's Law, including the placement of the constant in the law. You may assume that you know Coulomb's Law. 2. [From homework] Two charges, -Q and - |alpha| Q are a distance L 0 0 apart. These two charges are free to move but do not because there is a third charge nearby. What must be the charge and placement of the third charge for the first two to be in equilibrium? 3. Calculate the electric field everywhere inside a long cylinder of charge whose charge density is given by rho = b/r. The radius of the cylinder is R . 4. There are two large metallic sheets having charge densities of +sigma and -sigma a distance d apart. (a) Find the electric field between the plates. (b) What is the force exerted per unit area by the electric field near the center of the positively-charged plate? (c) What object is exerting this force? (d) What is the force exerted per unit area by the electric field near the center of an isolated, positively charged metallic plate? (e) If the answer to (d) is nonzero, what object is exerting the force? If the answer to (d) is zero, explain why the force vanishes here and does not vanish in question (b). [If you have not completed this question shortly before the papers are due, tell me what issues and options you are considering.]