Physics 1252 Exam #3E

Transcription

1 Phsics 1252 Eam #3E nstructions: This is a closed-book, closed-notes eam. You are allowed to use a clean print-out of our formula sheet, an scientific calculator, and a ruler. Do not write on our formula sheet, ecept for our name: it must be handed in, signed but clean, with our eam. There is space after each question to show our work; if ou need more space, ou ma use the back of the page, or request more paper. Please clearl indicate where our work for each problem is. Underline or draw a bo around our final answer. The eam consists of four sections. Read all the questions at the start so that ou can allocate our time wisel. Do eas ones first! You ma not share our calculator. The use of cell phones or an other electronic devices (besides calculators) is prohibited. All such gadgets must be turned off and put awa throughout the eam. Do not open the eam until told to begin. You have the one entire class period to finish the eam. Put our last name on ever page of the eam and on the formula sheet. You must provide eplanations and/or show work legibl to receive full credit for Sections, and V. Make sure that our answers include appropriate units and significant digits. (Note: or intermediate steps in our calculation, it s best to carr more significant digits.) undamental constants and unit prefies are on the ormula Sheet, last page. signing below, ou indicate that ou understand the instructions for this eam and agree to abide b them. You also certif that ou will personall uphold the universit s standards of academic honest for this eam, and will not tolerate an violations of these standards b others. Unsigned eams will not be graded. Signature: UGACard #: Copright c 2016 Universit of Georgia. Unauthoried duplication or distribution prohibited.

2 Section V (onus) Score /30 /35 /35 /10 : Multiple-Choice Questions (30 points) or each question below, choose the single best response and write the corresponding capital letter in the bo provided. There is no penalt for guessing the wrong answer. 1. Two ver thin circular rings, labeled 1 and 2 in the following, with radii R 1 and R 2, respectivel, and R 1 > R 2, are both centered at the coordinate origin O (0, 0, 0), as shown in the drawing. Ring 1 lies in the -plane with current flowing around the ring in the direction indicated in panel () of the drawing. Ring 2 lies in the -plane with current flowing around the ring in the direction indicated in panel (C) of the drawing. ig (A) () (C) Plane View --Plane View --Plane View Let 1 > 0 and 2 > 0 denote the magnetic field strengths produced at the origin O b onl and onl, respectivel. The total magnetic field vector (,, ) produced b both currents at the origin O is then given b: A. (,, ) = (0, 1 2, 0). (,, ) = (0, 1 + 2, 0) C. (,, ) = ( 2, 0, + 1 ) D. (,, ) = (+ 2, 0, 1 ) E. (,, ) = ( 2, 0, 1 ) Copright c 2016 Universit of Georgia. 2

3 2. A piece of straight wire carring a current,, is subjected to a uniform magnetic field,. Which one of the following figure panels could correctl represent the wire, its current flow direction, the -field direction and the direction of the magnetic force,, eerted on the wire b the magnetic field? ig (A) () (C) (D) (E) A.. C. D. E. 3. A molecular ion beam containing four different tpes of ions, called P, Q, R and S here. The beam enters a uniform magnetic field, as shown in drawing below, with 0 above the lower horiontal line, and perpendicular to, and pointing out of, the plane of the drawing. The incident straight beam is in the plane of the drawing. ig (out) R Q P S =0 The diameters of the semicircular ion trajectories in the -field, denoted b d P, d Q, d R and d S, respectivel are observed to be in a ratio of d P : d Q : d R : d S = 1 : 2 : 3 : 4, as indicated in the drawing. Assume all four ion tpes carr the same absolute amount of charge per ion, q, and the all enter the -field with the same kinetic energ K. (Hint/Warning: K = 1 2 mv2. Epress v in terms of K!) What is the ratio of the ion masses, denoted b m P, m Q, m R and m S, respectivel? A. m P : m Q : m R : m S = 1 : 1 : 1 : m P : m Q : m R : m S = : 2 1 : 3 1 : 4. C. m P : m Q : m R : m S = 1 : 4 : 9 : 16. D. m P : m Q : m R : m S = 1 : 2 : 3 : 4. E. m P : m Q : m R : m S = 1 : 2 : 3 : 4. Copright c 2016 Universit of Georgia. 3

4 4. A wire of some length L and with a circular cross-section of diameter D, made out of a material with an electrical resistivit ρ, has a resistance of 250 kω. What will be the resistance of a wire of length 15L and diameter 5D, made from a different material, with a resistivit 2ρ? A. 300 kω. 75 kω C kω D kω E kω 5. Three different circuits, Z, Y and X, are built with the same three resistors, R 1, R 2, and R 3, and the same batter of batter voltage E, as shown in the drawing. Compare and rank the magnitude of the voltage drops V 1 across R 1, observed in the three different circuits. ig o 3 R 3 o R 1 o R 2 E R 2 E R 2 E 3 R 3 R 1 3 R 3 R 1 (Z) (Y) (X) A. V 1 (Y ) < V 1 (X) < V 1 (Z). V 1 (Z) < V 1 (X) < V 1 (Y ) C. V 1 (Z) < V 1 (Y ) < V 1 (X) D. V 1 (X) < V 1 (Z) < V 1 (Y ) E. V 1 (X) < V 1 (Y ) < V 1 (Z) 6. n circuit Y in ig.3.33, two of the resistances are R 1 = 10 Ω and R 2 = 20 Ω; and two of the currents are = 5A and 3 = 2A. What is the batter voltage E? A. 10V. 190V C. 90V D. 110V E. 200V Copright c 2016 Universit of Georgia. 4

5 : Circuit Analsis (35 points) n the circuit shown below, assume that = 2A, 4 = 4A, R 1 = 7Ω, R 2 = 6Ω, R 3 = 8Ω, C = 50 µ. Also assume that the capacitor is full charged, b the voltage drop across it, the left capactor plate carries a charge of Q = +200µ and there is no current flowing to or from either capacitor plate. ig p o a R 1 R 2 E C C 3 R 3 R C 4 R 4 q b (a) ind the electric potential difference, V V, between check points and. (b) ind the total current, o. [Hint: Use a loop to find, then a junction to find o.] (c) ind the batter voltage E. [Hint: Use a junction to find 3, then a loop to find E.] (d) How much heat is generated in resistor R C during 1 hour? Copright c 2016 Universit of Georgia. 5

6 Work Space for Problem : Copright c 2016 Universit of Georgia. 6

7 : Magnetic ields and orces (35 points) Two ver long thin straight wires running parallel to the -ais and cutting through the -ais at 1 = 4m and through the -ais at 2 = 5m, respectivel, carr currents and, both in the -direction, as shown in drawing below. is 6 times as strong as. The two currents produce magnetic field contributions 1 and 2, respectivel, at point P (5m, 4m, 0m) in the -plane. --Plane View P ig (a) What is the absolute value of the angle between the +-direction and the total magnetic field vector, = 1 + 2, produced b the two currents at point P? (Hint: You onl need the field strength ratio, 1 / 2!) (b) f the total magnetic field strength at point P is = 3.2µT what are and? (c) Suppose an electron is shot through point P in the -direction with a speed of m/s. ind the electron s acceleration vector, a (a, a, a ) at P, due to the magnetic force. State all three cartesian components of a. [Hint: Use the same direction and strength of as found in (a) and given in (b), respectivel.] Copright c 2016 Universit of Georgia. 7

8 Work Space for Problem : Copright c 2016 Universit of Georgia. 8

9 V: More Magnetic orce (10 points, onus) Suppose the two current-carring wires in Problem are both 150m long, the current is 7A and the ratio of the two currents is the same as given in Problem. ind the magnetic force eerted b wire 1 on wire 2. State the strength of that force,, and the angle between and the +-direction. Copright c 2016 Universit of Georgia. 9