Physics 1252 Section Exam #2A

Transcription

1 Thu, 23 March 2017 Name: Physics 1252 Section Exam #2A Instructions: This is a closed-book, closed-notes exam. You are allowed to use a clean print-out of your formula sheet, any scientific calculator, and a ruler. Do not write on your formula sheet, except for your name: it must be handed in, signed but clean, with your exam. There is space after each question to show your work; if you need more space, you may use the back of the page, or request more paper. Please clearly indicate where your work for each problem is. Underline or draw a box around your final answer. The exam consists of four sections. Read all the questions at the start so that you can allocate your time wisely. Do easy ones first! You may not share your calculator. The use of cell phones or any other electronic devices (besides calculators) is prohibited. All such gadgets must be turned o and put away throughout the exam. Do not open the exam until told to begin. You have the one entire class period to finish the exam. Put your last name on every page of the exam and on the formula sheet. You must provide explanations and/or show work legibly to receive full credit for Sections II and III. Make sure that your answers include appropriate units and significant digits. (Note: For intermediate steps in your calculation, it s best to carry more significant digits.) Fundamental constants and unit prefixes are on the Formula Sheet, last page. By signing below, you indicate that you understand the instructions for this exam and agree to abide by them. You also certify that you will personally uphold the university s standards of academic honesty for this exam, and will not tolerate any violations of these standards by others. Unsigned exams will not be graded. Signature: UGACard #: Copyright c 2017 University of Georgia. Unauthorized duplication or distribution prohibited.

2 Section I II III IV (Bonus) Score /20 /40 /40 /10 I. Multiple-Choice Questions (20 points) For each question below, choose the single best response and write the corresponding capital letter in the box provided. There is no penalty for guessing the wrong answer. 1. If two point charges Q 1 and Q 2 at some distance r repel each other with a force of 10µN, what force would they exert on each other if Q 1 is tripled ( 3) without change of sign; r is doubled ( 2), and the sign of Q 2 is reversed? The two charges will A. repel each other with a force of 15µN B. attract each other with a force of 15µN C. repel each other with a force of 7.5µN D. attract each other with a force of 13.33µN E. attract each other with a force of 7.5µN 2. In a septuple slit (7-slit) interference experiment, a 4 th order principal intensity maximum is observed at an angle 4 = o, measured from the central axis, and sin 4 =0.64. How many principal maxima, total, including the central maximum, can be observed across the entire, very wide (infinite-width) screen, i.e., between = 90 o and =+90 o? A. 7 B. 14 C. 12 D. 13 E. 15 Copyright c 2017 University of Georgia. 2

3 3. In the figure below, Q 1 is a positive and Q 2 is a negative point charge with Q 1 and Q 2 being of comparable magnitude. Which arrow drawn at P could correctly represent the electric field vector ~ E generated by Q 1 and Q 2 at P? P Fig Q 2 (D) (E) (C) (B) (A) Q 1 A. B. C. D. E. 4. A di raction grating (in air or vacuum), is illuminated by coherent (laser) light with wavelength and wave oscillation period = /c. The third order intensity maximum, to the right of the central intensity maximum M, islocatedatpointq, as shown in the figure below. A wave crest A, fromslitr, andawavecrestb, from the neighboring slit S to the right of R, havedepartedatthesametimefromtheir respective slits of origin. Therefore, at Q, M Q Fig R S Diffr. Grating Laser Beam A. A and B will arrive at the same time. B. B will arrive 3 periods before A. C. B will arrive 5/2 periodsbeforea. D. A will arrive 3 periods before B. E. B will arrive 4 periods before A. Copyright c 2017 University of Georgia. 3

4 II. Force and Electric Field from Point Charges (40 points) Two point charges, Q 1 = 7.2mC and Q 2 =+4.8mC, are positioned at x 1 = 0.6m and at x 2 =+0.4m, respectively, on the x-axis. For each part below, (a), (b), (c), you have to make a separate clean, BIG drawing to get full credit for the problem, see next page. (a) A small test charge, q = µc, is placed on the x-axis at x q = 0m. Find the net force exerted on q, jointlybyq 1 and Q 2. State all three components of the force vector, ~F =(F x,f y,f z ), and state the magnitude of the force, F = ~ F. [20points] (b) Find the electric field generated jointly by Q 1 and Q 2 at a point P,locatedatx P = 0.2m on the x-axis. State all three components of the electric field vector, ~ E = (E x,e y,e z ), and state its magnitude, E = ~ E. [15points] (c) Repeat part (a), if Q 1 and Q 2 are moved to the new locations (x 1,y 1,z 1 )=(0.4, 0.3, 0)m and (x 2,y 2,z 2 )=(0, 0.4, 0)m, in the x-y-plane, with all other input parameters remaining unchanged. [5 points] Copyright c 2017 University of Georgia. 4

5 Three Drawings, for Problem II (a), (b) and (c): Your drawings do not have to be to scale, but they must show locations of charges and/or observation points (P )onthecorrectsideofthex-axis and/or in the correct quadrants of the x-y-plane. Tail ends of force vectors should be drawn to co-incide with the location of the object the force is being exerted on (free body diagram). Tail ends of electric field vectors should be drawn to co-incide with the location of the observation point (P )where the electric field vectors are generated. (a) Your drawing must show the locations of the charges, and the force vectors ~ F 1 exerted only by Q 1 on q, ~ F 2 exerted only by Q 2 on q, andthenetforce, ~ F. (b) Your drawing must show the locations of the charges, and the field vectors ~ E 1 generated only by Q 1 ; ~ E 2 generated only by Q 2 ;andthenetfieldvector ~ E. (c) Follow instructions for part (a) and also draw the vectors ~r 1 and ~r 2 from Q 1 and from Q 2 to q, respectively. Copyright c 2017 University of Georgia. 5

6 III. Two-Source Interference (40 points) Two small microwave sources, oscillating at the same frequency and in phase, are positioned 8m to the left of the y-axis, 3cm above and 3cm below the x-axis, respectively. A microwave detector, P,movingupalongthey-axis, observes a maximum in microwave intensity at y 0 = 0m, and, closest to that, an intensity minimum, aty 1/2 =3.640m, if the experiment is performed in air, with an index of refraction n A = (a) Draw this: big, on full blank page attached! Show: x-, y-axes, detector, sources, line connecting sources, observation angle, allgivendistances.itneednottobetoscale. Then find the oscillation frequency of the sources. [20 points] (b) How many intensity maxima, total, and how many intensity minima, total, will the detector observe if it travels upward along the y-axis from very far below (y = 1) to very far above the x-axis (y =+1)? [15 points] (c) If the entire experimental apparatus (sources, detector, and the entire space in between sources and y-axis) is now submerged in a transparent liquid, the intensity minimum, closest to the central maximum, is observed on the y-axis at y 1/2 =2.273m. What is the index of refraction of this liquid for microwaves? Hint: the frequency of the sources, the spacing between them, and their distance from the y-axis is the same as before; but the speed of wave propagation is not. [5 points] Copyright c 2017 University of Georgia. 6

7 Drawing for Problem III (a): Copyright c 2017 University of Georgia. 7

8 IV. Electric Field Vector in the x-y-plane (10 points, Bonus) Repeat part (b) of Problem II, if Q 1 and Q 2 are moved to the new locations (x 1,y 1,z 1 )= (0.4, 0.3, 0)m and (x 2,y 2,z 2 )=(0, 0.4, 0)m, respectively, in the x-y-plane, with all other input parameters remaining unchanged. Don t forget the drawing, next page! Copyright c 2017 University of Georgia. 8

9 Drawing for Problem IV: Follow detailed drawing instructions given above for drawings in Problem II (b). Also draw the vectors ~r 1 and ~r 2 from Q 1 and from Q 2 to P,respectively. Copyright c 2017 University of Georgia. 9