EXAM 1 March 13, 1991 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). 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. 2. A charge of -3Q is at the origin of coordinates. Where must a charge +Q be placed on the x axis if the combined field is to be zero at a point x = +b on the axis? 3. A proton (mass m ) is shot out along the x p axis from the origin with a speed v . In 0 this region, there is a constant electric field of magnitude ^ E pointed in the -x direction. How far from the origin does the proton get before it stops? 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.]