Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

P216 final exam Apr. 11, 2000 Page 1 of 4 UNIVERSITY OF VICTORIA EXAMINATIONS APRIL 2000 PHYSICS 216 S01 TO BE ANSWERED IN BOOKLETS DURATION: 3 Hours INSTRUCTOR: R. V. Kowalewski STUDENTS MUST COUNT THE NUMBER OF PAGES IN THIS EXAMINATION PAPER BEFORE BEGINNING TO WRITE, AND REPORT ANY DISCREPANCY TO THE INVIGILATOR. THE NUMBER OF PAGES IN THIS QUESTION PAPER IS INDICATED IN THE HEADER AT THE TOP OF EACH PAGE. The examination will be graded out of 100 points. Students are allowed to bring one formula sheet (one side of an 8½ x 11 page) and a calculator. P216 final exam Apr. 11, 2000 Page 2 of 4 (25 pts) Question 1 - short answers (a) Lines of magnetic flux always form closed loops - true or false? (b) How much energy (in eV) is required to bring two electrons from an infinite separation to a separation of 0.1 nm? (c) A hoop of area A is rotating around the z axis with angular velocity = k in the presence of a B field oriented along the +x axis. If the hoop is in the y-z plane at time t = 0, graph the induced EMF as a function of time between t = 0 and t = 2/ (be sure to label the axes clearly). (d) Does the revolution frequency of a charged particle in a uniform magnetic field depend on the particle’s energy? (e) Graph the electric field produced by a hollow conducting spherical shell of radius R containing charge Q as a function of the distance r from the center of the spherical shell. Label the axes. (f) Explain how the Hall voltage can be used to measure the drift velocity of the charge carriers in a sample. (Give me an equation and a drawing!) (g) A coil of wire is rotated in a magnetic field. The ends of the wire from the coil are connected by a resistor. Does the mechanical torque needed to rotate the coil depend on the size (in Ohms) of the resistor? (h) What limits the maximum magnetisation M that can be achieved in a particular substance? (15 pts) Question 2 A conducting bar is sliding along frictionless conducting rails. The rails are connected by a resistance R which is large compared to the resistance of the rails and of the sliding bar. A uniform B field is oriented perpendicular to the plane containing the bar and the rails as shown. (a) Find the magnitude of the induced EMF as a function of the speed v of the sliding bar. (b) In what direction (clockwise/counterclockwise) is the induced current? (c) What force must be supplied to keep the bar moving at speed v? (d) Show that the power supplied to keep the bar moving (i.e. work per unit time) is equal to the power dissipated in the resistor. y x v Binto page R L P216 final exam Apr. 11, 2000 Page 3 of 4 (15 pts) Question 3 Consider a cylindrical capacitor consisting of an inner conductor of radius a, an outer conductor or radius b, and a length L >> b. The capacitor is initially connected to a battery that provides a potential difference V0. (a) Find the electric field in the region between the conductors. (b) How much charge is stored on the inner conductor if the material between the conductors is air? (c) A material with dielectric constant is inserted into the gap between the conductors. What happens to the energy stored in the capacitor? Calculate the ratio U / Uair . (d) The capacitor is now disconnected from the battery. The dielectric material is then removed. Find the potential difference between the plates, written in terms of the initial voltage V0. (15 pts) Question 4 J. J. Thomson discovered the electron using a cathode ray tube (we now know that the particles given off by such a tube are electrons), a velocity selector (crossed E and B fields) and a fluorescent screen as shown. Assume the beam contains monoenergetic particles. For simplicity assume w/L<<1 so you can use y = L tan as the deflection, where is the exit angle w.r.t. the initial beam when the particle leaves the region of width w. Further assume the is small (<0.1) so that sin tan. Find in terms of B, E, w and L: (a) the velocity producing no deflection when E is switched on (b) the deflection at the screen for electrons when E is switched off (c) Produce a set of values for E, B, w and L that would produce no deflection at the screen with E on and a 1 cm deflection with E off. Make experimentally reasonable choices and be sure to satisfy the constraints assumed above on and w/L. Note that me = 9.11*10-31kg. (d) If the particle beam contains a range of velocities, what might one expect to see with E on and with E off? particle beam Eup screen Bout w L P216 final exam Apr. 11, 2000 Page 4 of 4 (15 pts) Question 5 (a) Use Ampère’s Law to determine the magnetic field inside a long solenoid of circular cross-section. Explain what you are doing. The number of turns per unit length is n, the current in the windings is I and the cross-sectional area is A. (b) The solenoid from part (a) is now formed into a square cross-section without changing the number of turns per unit length and with the perimeter of each square winding equal to the circumference of the initial circular winding. Explain why the B field inside the solenoid remains unchanged. (c) Calculate the inductance per unit length for both cases. Remember that you were already told that B is the same in both configurations. Express your answer in terms of the quantities given above and fundamental constants. (d) Calculate the change in stored energy per unit length in going from circular to square cross-section. (15 pts) Question 6 Consider a current loop of radius a carrying current I as shown. Show that the magnetic field at point P can be written B = -0 / (2d3) where is the magnetic moment of the loop and d is the distance from P to the center of the loop. The point P is in the plane containing the loop, and d>>a. Use the Biot-Savart Law (explain clearly what you are doing!) and use d>>a to simplify the integrand before evaluating the integral. It may help to recall the law of cosines for the triangle shown, namely r2 = d2 + a2 - 2ad cos. y x angle (between sides of length a and d) I a P d