Problem Score 1 /30 2 /15 3 /15 4 /20 5 /20 6 /20 7 /15 8 /25 9 /20 10 /20 Total /200

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1 PHYS 2114 Final Exam December 15, 2005 Time of Discussion Section: Name: Instructions: Do not open exam until so instructed. Write name and discussion time above; do not write anything in table at right. For maximum credit, show your work; you may also draw a diagram, give a brief discussion, or explain what you did (or would do). You may use a calculator and only the information sheet handed out with the exam. The points listed add to 200. You have one hour and 50 minutes. Problem Score 1 /30 2 /15 3 /15 4 /20 5 /20 6 /20 7 /15 8 /25 9 /20 10 /20 Total /200 The information sheet (front and back) is being handed out separately. Final exam grades will be entered into WebAssign, and it will display an overall percentage grade and the corresponding letter grade. This grade is unofficial. Your official course letter grade, which may differ from that displayed by WebAssign, will be available to you through the University s online student information system by Dec. 21. Solutions will not be posted, but students who wish to see the solutions and look over their exams are welcome to make an appointment to see Dr. Rosenberger anytime after Dec. 20. Exams have to be kept for a semester, but students who want their exams returned can pick them up at the end of spring semester.

2 1. (30 points) Two charges are located on the coordinate axes as shown; q 1 = 400 nc and q 2 = -225 nc. y (a) (10 points) Find the magnitude of the net electric field that the charges produce at the origin. 4 cm q 1 q 2 3 cm x (b) (10 points) Find the net electric potential at the origin. (c) (10 points) Find the potential energy of this charge distribution.

3 2. (15 points) For parts (a) and (b): Charge is distributed along the y axis from L/2 to L/2. The linear charge density is λ. y (a) (5 points) Write an expression for the (approximate) magnitude of the electric field at a point on the x axis, for the case where x << L. L x (b) (5 points) Write an expression for the (approximate) magnitude of the electric field at a point on the x axis, for the case where x >> L. (c) (5 points) You are told that the potential at a point a large distance from an electric dipole 1 p is given by the expression V ( r) =. Determine whether this point is on the dipole s axis 2 4πε 0 r or in its bisecting plane.

4 3. (15 points) A solid conducting sphere of radius a has a charge Q. It is surrounded by a concentric spherical conducting shell (very thin) of radius b, having charge Q. Use Gauss s Law to find expressions for the magnitude of the electric field at all points, that is, for r < a, for a < r < b, and for r > b. a b

5 4. (20 points) (a) (4 points) A long uniform wire has a resistance of 1.0 Ω. If the wire s length is halved, how will its resistance change? How will its resistivity change? For parts (b) and (c): A long straight wire is carrying a current I. At the point P, the magnetic field due to that current has a value of 2.50 mt, out of the page. (b) (8 points) Find the value of I and specify its direction by drawing an arrowhead on the wire. 5cm P (c) (8 points) An electron is at point P, approaching the wire with a speed of m/s. Find the magnitude and direction of the force on the electron due to the wire s magnetic field.

6 5. (20 points) In the circuits shown here, the switch has been open for a long time, so no current is flowing. (a) (10 points) (i) Immediately after closing the switch, what is the current in the 10-Ω resistor? (ii) After the switch has been closed for a long time, what is the current in the 10- Ω resistor, and what is the energy stored in the capacitor? 50 μf (b) (10 points) (i) Immediately after closing the switch, what is the current in the 10-Ω resistor? (ii) After the switch has been closed for a long time, what is the current in the 10- Ω resistor, and what is the energy stored in the inductor?

7 6. (20 points) For four points each, answer the following: (a) Describe the equipotential surfaces in the vicinity of an infinite sheet of charge. For these next four parts, just give a short answer (one or a few words, no explanation). (b) Should a voltmeter have high resistance or low resistance? (c) When the switch is closed, does bulb A get brighter, dimmer, or not change in brightness? (d) Which electric potential graph describes this electric field? (Circle the correct answer.) (e) A solid conducting sphere, 5 cm in diameter, is in electrostatic equilibrium. Its surface is at a potential of 50 V. If this is enough information to determine the potential at the center of the cube, give its value; if not, circle the following: not enough information.

7. (15 points) A zero-resistance conducting bar slides on zero-resistance conducting rails in a uniform magnetic field (B = 2.0 T) perpendicular to the plane of the rails (out of the page).

8 7. (15 points) A zero-resistance conducting bar slides on zero-resistance conducting rails in a uniform magnetic field (B = 2.0 T) perpendicular to the plane of the rails (out of the page). Its speed is constant, because it is acted on by an external force; the magnetic force on the bar (F mag = 20 mn) is shown in the figure. 5.0 Ω 50 cm F mag (a) (5 points) What is the direction of the induced current in the circuit and which direction is the bar sliding (be specific)? (b) (10 points) Find the speed of the bar.

9 8. (25 points) (a) (15 points) A diffraction grating, consisting of many slits spaced 2.00 μm apart, is embedded in a rectangular block of plastic that has an index of refraction n = Light of wavelength 560 nm (in air) is incident normal to the block face and to the grating. Find the lowest diffraction order m that will be totally internally reflected at the exit face. (b) (10 points) Standing-wave modes are set up in two tubes and produce sound waves heard by an observer. Tube 1 is 34.3 cm long, is open at both ends, and produces its second harmonic. Tube 2 is 25.8 cm long, is open at one end and closed at the other, and produces its third harmonic. What beat frequency is heard?

10 9. (20 points) (a) (10 points) An object is a distance 2f from a lens of focal length f (> 0). Find the position and magnification of the image formed. Is it real or virtual? Sketch a ray diagram showing the three principal rays. (b) (10 points) An electromagnetic wave has an electric field amplitude of E 0 = V/m. Find the intensity of this wave, and find the amplitude of its magnetic field, BB0.

11 10. (20 points) A fish inside a spherical fishbowl (radius 20 cm; n water = 1.33 = 4/3; negligibly thin wall) is 5 cm from the wall. Find the position, magnification, and character (real or virtual) of the image of the fish seen by a cat outside the fishbowl.

Final Exam. PHY2049 Fall11

Final Exam. PHY2049 Fall11 Exam 1. Three charges form an equilateral triangle of side length d = 2 cm. The top charge is q3 = 3 μc, while the bottom two are q1 = q2 = - 6 μc. What is the magnitude of the net force acting on q3?