Physics 1252 Exam #2A

Transcription

1 Physics 1252 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 off 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 2016 University of Georgia. Unauthorized duplication or distribution prohibited.

2 Section I II III IV (Bonus) Score /30 /35 /35 /10 I: Multiple-Choice Questions (30 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 20µN, 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 30µN C. attract each other with a force of 26.67µN D. attract each other with a force of 15µN E. repel each other with a force of 30µN 2. In a quadruple slit (4-slit) interference experiment, a 3 rd order principal intensity maximum is observed at an angle θ 3 = o, measured from the central axis, and sin θ 3 = How many principal maxima, total, including the central maximum, can be observed across the entire, very wide (infinite-width) screen, i.e., between θ = 90 o and θ =+90 o? A. 11 B. 10 C. 9 D. 7 E A muon is a sub-atomic particle with the same charge as an electron. If a muon is released, initially at rest, at a distance r from a spatially fixed negative point charge, Q, the muon will accelerate to a final speed, v, at a very large (infinite) distance from the point charge. What would be the muon s final speed, v, if instead it were released, initially at rest, at a distance r = 4r from a negative point charge, Q = 7Q? A. v = 49 v 16 B. v = 7 v 2 C. v = 7 v 4 D. v = 2 7 v E. v = 7 4 v Copyright c 2016 University of Georgia. 2

3 4. In the figure below, Q 1 and Q 2 are positive point charges with Q 2 > Q 1. Which arrow drawn at P could correctly represent the electric field vector E generated by Q 1 and Q 2 at P? P (C) Q 2 (D) (E) (B) (A) Fig Q 1 A. B. C. D. E. 5. Two large, metallic, planar, parallel, charged capacitor plates have an electric potential difference of V 1 V 2 = +7500V, where V 1 and V 2 are the electric potentials on the top and bottom plate, respectively, as shown here: Plate 1 Plate 2 Fig An electron is shot through a small hole in the bottom plate, into the space between the two plates. The electron, while traveling from the bottom to the top plate,... A. will lose J in kinetic energy between bottom and top plate. B. will gain J in kinetic energy between bottom and top plate. C. must have a kinetic energy of at least J, as it passes through the bottom plate, in order to reach the top plate. D. will gain J in kinetic energy between bottom and top plate. E. will gain J in kinetic energy between bottom and top plate. Copyright c 2016 University of Georgia. 3

4 6. A diffraction grating (in air or vacuum), is illuminated by coherent (laser) light with wavelength λ and wave oscillation period τ = λ/c. The 5th order intensity maximum, to the right of the central intensity maximum M, is located at point Q, as shown in the figure below. A wave crest A, from slit R, and a wave crest B, from the neighboring slit S to the right of R, have departed at the same time from their respective slits of origin. Therefore, at Q, M Q Fig R S Diffr. Grating Laser Beam A. B will arrive 6 periods before A. B. B will arrive 9/2 periods before A. C. B will arrive 5 periods before A. D. A will arrive 5 periods before B. E. A and B will arrive at the same time. Copyright c 2016 University of Georgia. 4

5 II: Two-Source Interference (35 points) Two small microwave sources, oscillating at the same frequency and in phase, are positioned 11m below the x-axis, 2cm to the left and 2cm to the right of the y-axis, respectively. A microwave detector, P, moving along the x-axis, observes a maximum in microwave intensity at x 0 = 0m, and, closest to that, an intensity minimum, at x 1/2 = 2.500m, 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 θ, all given distances. It need not to be to scale. Then find the oscillation frequency of the microwave sources. (b) How many intensity maxima, total, and how many intensity minima, total, will the detector observe if it travels along the x-axis from very far to the left (x = ) to very far to the right (x = + )? (c) If the entire experimental apparatus (sources, detector, and the entire space in between sources and x-axis) is now submerged in a transparent liquid, the intensity minimum, closest to the central maximum, is now observed on the x-axis at x 1/2 = 1.800m. 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 x-axis is the same as before; but the speed of wave propagation is not. Copyright c 2016 University of Georgia. 5

6 Drawing for Problem II (a): Copyright c 2016 University of Georgia. 6

7 III: Electric Field from Point Charges (35 points) Four point charges of unknown charge amounts, Q 1, Q 2, Q 3, Q 4, are positioned at various unknown locations in the x-y-plane. They jointly produce a net electric field vector E o [E o,x, E o,y, E o,z ] with components E o,x = +6.5N/C, E o,y = 3.5N/C, E o,z = 0, at an observation point, P (x P, 0, 0) with x P = 3m, on the x-axis. A fifth point charge, Q 5 = +25nC, is now added on the x-axis at x 5 = +2m and all five point charges, Q 1, Q 2, Q 3, Q 4, Q 5, then jointly produce a net electric field, E = [E x, E y, E z ]. (a) Draw this: big, on full blank page attached! Show: x-axis, y-axis, Q 5, P, and E o. Also show the field contribution E 5, produced by Q 5 at P. Draw both E o and E 5 with their tail ends attached to P. It does not have to be to scale, but all vectors must point into the correct quadrant or along the correct coordinate axis direction. (b) Calculate the components of E at P ; its strength, E ; and its angle, θ, measured from the +x-direction, with θ > 0 if E points above the x-axis, else θ < 0. Then also show E in the drawing from (a), as the resultant in a vector addition parallelogram. (c) Now Q 5 is removed again and an electron is placed at point P and then released, to accelerate subject to the electric field produced by the other four point charges. Find the electron s acceleration, a, immediately after its release at P. State the magnitude of the acceleration, a, and its angle, φ, measured from the +x-direction, with φ > 0 if a points above the x-axis, else φ < 0. Then also show a in the drawing from (a), correctly aligned with the relevant electric field vector. Copyright c 2016 University of Georgia. 7

8 Drawing for Problem III (a): Copyright c 2016 University of Georgia. 8

9 IV: Speeding Up the Electron (10 points, Bonus) Suppose the electron in Part III(c) is shot directly at the spatially fixed point charge Q 5 = +25nC, with all other charges (Q 1, Q 2, Q 3, Q 4 ) having been removed. At a very large initial distance (r i = ) from Q 5, the electron s initial speed is very small, v i = 0m/s. How close to Q 5 must the electron get in order to reach a speed of v f = 600, 000m/s? State this distance, r f, in units of meters. Copyright c 2016 University of Georgia. 9