EXAM 1 March 6, 1996 PS 208 YOUR NAME:________________________________________________ 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] (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. For the remaining problems, place the equations representing the physics principles you are using in the box on the page. You may use and English label for the principle, the general form of the equation, or the form you get applying the principle to the problem at hand. Each question counts 30 points. 2. 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 F. tot Diagram, if any: Principles: ____________________________________________________ | | | | | | | | | | | | | | | | | | | | | | |____________________________________________________| 3. (a) What is the potential difference between two cylinders each of length L, when there is a charge +Q on the outer cylinder and -Q on the inner. The radii of the inside and outside cylinders are R and R respectively. 1 2 Diagram: Principles: ____________________________________________________ | | | | | | | | | | | | | | | | | | | | | | |____________________________________________________| 4 (From homework). A solid nonconducting sphere of radius r has a total charge Q which is distributed according 0 to rho = br , where rho is the charge per unit volume (charge density) and b is a constant. Determine the electric field at all points inside the sphere. Notice that rho cannot be taken out of radial integrations, but is a constant with respect to angular integrations. [If you have trouble with dV, write out the closest form you can and box it so I will know what you are using.] Diagram: Principles: ____________________________________________________ | | | | | | | | | | | | | | | | | | | | | | |____________________________________________________| Use this page to continue # 4.