EXAM 3 March 7, 1990 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. (10 points) 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. (The remaining problems count 30 points each.) 2. (From homework) A very long solid nonconducting cylinder of radius R and length L (with R << L ) possesses a uniform 0 0 volume charge density rho. Determine the electric field for all points inside the cylinder (r < R ). 0 3. A thin charged rod of length L lies along the positive x axis with one end at the origin. Its charge per unit length is lambda = A x , where A is a constant. Find the electric field at a point on the x axis, with x = b + L . [Integration hint: you may find it useful to make a change of variables to make the denominator in the integrand as simple as possible.] 4. A small sphere of mass m and charge q hangs as a pendulum of length L in a region where the electric field is directed downward and has magnitude E . Show that the period of the pendulum is omega = sqrt(L/[ g + qE/m ]) . [Note that the expression for omega under gravity alone is contained in this expression.]