PHYS 220 Final, Spring 2008

Physics 220 Final Exam Time : 2:30 hrs. #1. Using appropriate diagrams and reasoning, define the following terms: a) Magnetization curve b) Hysteresis, coercive force, remanence point. c) Spontaneous magnetization, Curie temperature. d) Ferromagnetic , antiterromagnetic and Ferrimagnetic. Two circular plates of radius(a) separated by a distance (d) form an ideal capacitor : Assume that the dielectric is a perfect insulator with uniform D-fieid (i.e. neglect the fringing field at the edge of the plates). The capacitor is being charged by a constant current I. (a) Find the H-field at a point P on the cylindrical surface of the dielectric. (b) Find the magnitude and direction of the Poynting vector S:at::P. >_> (c)Integrate S.n over the cylindrical surface of the dielectric, and show that the result is equal to the time rate of change of the stored electrostatic energy. #3. A through of infinite length is contructed of thin conducting sheets whose cross section is shown ‘ V=e7 Conductor in the adjacent figure. ; . A conducting lid is mt placed at x = a , with < small gaps between the lid and the trough. . Prae tw to If e. = 0 within. the <— Conductor cap trough, V = V, on the Vevloy) Va Vs lid , and V = 0 on the three trough wails, P 7 — xf find the expression for V ao within the trough. (Hint: use Ved the method of separtion of variables in rectangular coordinates). a - A. The magnetic vector potential is giyen by A = ke where k and a are constants. Find B. - dy sin ax a Zz > ‘ B. Suppose we wish to produce a magnetic field of the form : H = K sin x ay where K is a constant . Find the current density that wiil produce this field. C. Consider the boundary between two perfect dielectrics, as shown in figure. Determine a relation between the angles 8 and Q,- Two spherical conductors are located in vacuum. mductor 1, of radius R, is grounded (i.e. at zero potential ). Conductor 2 is so small that it may be treated as a point charge. It bears the charge (q) and is located at a distande (d) from the grounded sphere. What is the charge induced on the grounded sphere ? (Use the method of images and the concept of coefficient of potential). #6. A closely wound long solenoid has a concentric magnetic rod inserted as shown: In the center region, — Find : REALE chase OAL te > Ave b a) H,B, M in both air and magnetic rod. > we b) Find Jig OF surface of rod 6000-60 mene and Sy within rod. or Q —? > #7. A spherical charge distribution has a volume charge density that is a function only of (r) , the distance from the center of the distribution, i.e. 9 = B(r). If p(r) is given as below, determine the electric field as a function of r. Integrate the result to obtain an expression for the electrostatic potential fx), subject to the restriction fer =0 a) p= 4 with A = constant for 0¢ r¢ R; p=0 for r>R b) & =P, (i.e. constant) for O<¢ r¢R e = 0 for r>R. #8. Find the force between a point charge (q) and an uncharged conducting sphere of radius (a). The point charge is located a distance (r) from the center of the sphere, where r > a. Find an approximate expression valid for r >> a. > #9. A uniform electric field E, is set up in a medium of dielectric constant K. Prove that the fieid insidé a spherical cavity in the medium is > > 3 KE E= ——2 2KkK+1 #10. A . Given a spherical charge distribution of radius R, uniform charge density y , Determine the self energy of the distribution by direct integration of i y- ¢ o(r) P(r) av + F Vo) Pix) aa. a4 5 B. A point charge q is located between two parallel, grounded, conducting planes which are separated by a distance (d). Find the locations of the infinite number of image charges. Express the force on charge (q) by an infinite series. é