2017 Final Examination Practice assignment PDF

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A practice examination given to students in the 2022 year....

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Physics 259 Final Exam, Winter 2017

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University of Calgary Faculty of Science Midterm test PHYSICS 259 ALL LECTURE SECTIONS

Version A April 20, 2017, 3:30-6:30 pm

Time: 180 minutes

This is a closed-book exam worth a total of 45 points. Please answer all questions.

ONLY THE FOLLOWING ITEMS ARE ALLOWED ON YOUR DESK DURING THE EXAM: 1. THIS MULTIPLE-CHOICE QUESTION BOOKLET, which includes the multiple-choice exam questions and the formula sheet (last page). THIS BOOKLET WILL NOT BE HANDED IN. Make sure this booklet contains 19 pages (including formula sheet). If you are missing any pages, get a new booklet from the exam supervisor. 2. A BUBBLE SHEET used to answer multiple-choice questions. IT WILL BE HANDED IN. IMPORTANT: START by entering your ID NUMBER, NAME and COURSE ID on the bubble sheet. Using a pen or a pencil, black out the corresponding numbers below your ID and name. DO THIS NOW. Then wait for the Exam Supervisor to signal when to start the test. All answers to the multiple-choice questions must be entered by blacking out the appropriate character (one of a, b, c, d, e) beside the question number on the bubble sheet. Make sure you darken the entire interior of the circle that contains the character. 3. A CALCULATOR: Schulich School of Engineering approved calculators. UNACCEPTABLE calculators include: cell phones, tablets, laptops, etc. 4. A PEN OR PENCIL, used to black out your answers on the bubble sheet. If you are using a PEN, make sure it is BLACK or BLUE in order to ensure the scanner reads your answers properly. PENCILS can also be used, but make sure you press firmly when answering so the scanner reads your answer properly. 5. YOUR STUDENT ID CARD. If you are missing anything from the above items, raise your hand and ask an exam supervisor to supply what is missing. If you are missing an item that should have been brought by you (e.g., calculator, pen/pencil) there is a limited supply of extras and are on a first come, first served basis. Please note that you cannot leave the room during the first and last 30 minutes of the exam. Students remaining during the last 30 minutes must remain seated for the duration of the exam until permitted to leave by the instructor.

Physics 259 Final Exam, Winter 2017

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Multiple Choice Questions (Total: 45 marks). Choose the BEST possible answer. 1. A circular conducting arc of radius R has a positive charge (+Q) evenly distributed, and a point charge located at distance R from the point P has charge +Q. In which direction is the net electric field at point P? a) b) c) d)

𝑗 −𝑗 𝑖 The electric field is zero

2. A pair of charged conducting plates produces a uniform electric field between the plates of 12,000 N/C, directed to the right. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial speed 𝑣0 = 2.0 ∙ 107 m/s as shown in the figure below. What is the final speed of the electron as it strikes plate B?

a) b) c) d)

𝑣𝑓 =

1.2 · 107 m/s 𝑣𝑓 = 1.5 · 107 m/s 𝑣𝑓 = 1.8 · 107 m/s 𝑣𝑓 = 2.1 · 107 m/s

3. Consider a spherical metal shell of inner radius R (as shown in the figure). A point charge of -3.5 mC is located at a distance R/2 from the centre of the shell. If the shell is neutral, what is the induced charge on its outer surface? a) + 3.5 mC, with uniform surface charge density b) zero c) +7.0 mC, with higher surface charge density on right side of the surface d) -3.5 mC, with uniform charge density.

Physics 259 Final Exam, Winter 2017

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2 + 𝑦3 − 𝑧 , where 𝑥, 𝑦, 𝑧 are measured in meters and 𝑉 is in Volts. What is the expression for the electric field in this region? 6 6 a) 𝐸󰇍 (𝑥, 𝑦, 𝑧) = − 3 𝑖 − 𝑗 − 𝑘

4. The electric potential in a certain region is given by:𝑉(𝑥, 𝑦, 𝑧) =

𝑥 1

b) 𝐸󰇍 (𝑥, 𝑦, 𝑧) = − 𝑖 − 𝑥 c) 𝐸󰇍 (𝑥, 𝑦, 𝑧) =

6

𝑥3 1

𝑖 +

d) 𝐸󰇍 (𝑥, 𝑦, 𝑧) = 𝑖 + 𝑥

𝑦4 1

2𝑦 2

6 𝑗 𝑦4 1

2𝑦 2

𝑥2

𝑗 − 2 𝑧 2 𝑘 1

+ 𝑘

𝑗 + 2 𝑧 2 𝑘 1

5. A nonconducting solid sphere has radius R = 1.64 cm with a total charge of q = +2.31 fC uniformly distributed through its volume. Take the electric potential at the sphere's center to be V0 = 0. What is V at a radial distance r = 1.20 cm from the center? a) b) c) d)

0.34 mV 0.68 mV 0.00 mV 0.23 mV

6. Three charges are placed in the corners of the equilateral triangle with side-length d as shown on the figure below. All charges are equal in magnitude, and their signs are indicated in the figure. What is the net force (magnitude and direction) on the charge located in the center of the triangle due to the other three charges? Note: the outer charges are placed equidistant from the center charge.

a) b) c) d)

3𝑞2

4𝜋𝜖0 𝑑2 𝑞2

4𝜋𝜖0 𝑑2 3𝑞2

2𝜋𝜖0 𝑑2 3𝑞2

2𝜋𝜖0 𝑑2

𝑖

𝑗

𝑗

𝑖

Physics 259 Final Exam, Winter 2017

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7. If we draw a circular Amperian loop of radius r inside a wire of radius R and length L that carries a uniform current density J, which of the following gives the amount of current enclosed by the Amperian loop?

a) b) c) d)

𝐼𝑒𝑛𝑐 = 2𝜋𝑅𝐿𝐽 𝐼𝑒𝑛𝑐 = 𝜋(𝑅 2 − 𝑟 2 )𝐽 𝐼𝑒𝑛𝑐 = 𝜋𝑟 2 𝐽 𝐼𝑒𝑛𝑐 = 𝜋𝑅 2 𝐽

8. Which of the following will NOT induce a current in a flat conducting loop sitting completely inside a region with a uniform magnetic field, regardless of the orientation of the loop? a) b) c) d)

Spinning the loop about an axis perpendicular to the magnetic field. Moving the loop in a direction perpendicular to the magnetic field. Changing the area of the loop. Changing the strength of the magnetic field.

󰇍 is zero around both loops, and I3 = 2 A, which 9. In the figure below, if the quantity ∮ 𝐵󰇍 · 󰇍𝑑𝑙 of the following statements is true?

a) b) c) d)

I1 = I2 = 1 A I1 = 4 A and I2 = 2 A I1 = 0 A and I2 = 2 A I1 = 2 A and I2 = 0 A

Physics 259 Final Exam, Winter 2017

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10. In the circuit below an ideal battery (electromotive force of 12 V), capacitor of 0.25 μF and two 2.0 Ω resistors are connected. What is the charge on the top plate of the capacitor after it has been fully charged? a) b) c) d)

3.0 µC -30 µC 30 µC –3.0 µC

11. When an initially uncharged capacitor is charged in an RC circuit, which is TRUE about its initial and final states? a) b) c) d)

It acts like an ordinary connecting wire throughout the charging process. It initially acts like a broken wire and finally acts like ordinary connecting wire. It acts like a broken wire throughout the charging process. It initially acts like an ordinary connecting wire and finally acts like a broken wire.

12. A real battery with internal resistance r = 5.0 Ω is connected to a circuit with a resistive load of R = 150 Ω as shown in the diagram. If the voltage across the terminals of the battery (labeled A and B) is 12.0 V, what is the power dissipated by the resistive load?

a) b) c) d)

0.96 W 0.80 W 0.75 W 0.59 W

13. A dielectric material is inserted between the plates of a charged capacitor. Which of the followings statements about the effects of the dielectric is TRUE? a) If the capacitor is not connected to a battery, the magnitude of the electric field between the plates increases. b) If the capacitor is connected to a battery, the charge on the plates remains constant. c) If the capacitor is not connected to a battery, the voltage between the plates remains constant. d) If the capacitor is not connected to a battery, the charge on the plates remains constant.

Physics 259 Final Exam, Winter 2017

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14. The figure below shows the graph of resistance R (y-axis) versus probe separation ∆L (xaxis) for a Play-Doh cylinder of total length 18 cm and diameter 24 mm, using a constant current of 50 mA. Based on the data provided, what is the resistivity of the Play-Doh?

a) b) c) d)

0.12 Ω · m 0.23 Ω · m 0.28 Ω · m 0.92 Ω · m

15. The resistor in the figure below has diameter D = 0.125 mm. The total resistance is R = 0.75 Ω and the resistivity of the silver (Ag), aluminum (Al), and tungsten (W) are as follows: ρAg = 1.59·10-8 Ω· m, ρAl = 2.82·10-8 Ω· m and ρW = 5.60·10-8 Ω· m. Based on the information provided what is the total length of the resistor?

a) b) c) d)

7.17 cm 30.7 cm 28.7 cm 9.18 cm

Physics 259 Final Exam, Winter 2017

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16. Which is TRUE about magnetic field lines? a) They begin on south poles and end on north poles, the same way electric field lines begin and end on positive and negative charges. b) They form closed loops directed away from a north pole and toward a south pole. c) They form closed loops directed away from a south pole and toward a north pole. d) They begin on north poles and end on south poles, the same way electric field lines begin and end on positive and negative charges. 17. Figure 1 below shows a schematic representation of the experiment used to determine the charge to mass ratio (e/m) of the electron. The magnetic field produced by the Helmholtz coils is B = 0.00147 T (pointing out of the page) and the electron beam follows a counter clockwise trajectory or radius r = 0.0365 m. Figure 2 is a schematic of the “electron gun” used to accelerate the electrons. What value of the potential difference was used to accelerate electrons if the e/m ratio determined in the experiment is 1.74·1011 C/kg?

a) b) c) d)

200 V 300 V 350V 250 V

18. A long solenoid has 110 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.61 cm perpendicular to the solenoid axis. The speed of the electron is 0.0416c (c = speed of light, equal to 2.998 × 108 m/s). Find the current i in the solenoid. a) b) c) d)

0.197 A 0.285 A 0.125 A 0.568 A

Physics 259 Final Exam, Winter 2017

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19. The switch S in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 16.8 μF through a resistor of resistance R = 22.8 kΩ. At what time is the potential across the capacitor equal to that across the resistor? a) b) c) d)

0.134 s 0.266 s 0.112 s 0.589 s

20. Which of the following statements about the self-induced emf of an inductor is TRUE? a) b) c) d)

It depends on the amount of current through the inductor. It depends on the rate at which energy is dissipated. It is a fixed value, depending on only the geometry of the device. It depends on the rate at which the current through it is changing.

21. The switch, S, in the figure below is closed at time t = 0. At what time is the current in the circuit equal to 2.40 A? (Select the closest answer.) a) b) c) d)

0.134 s 19.3 s 12.0 s 4.80 s

22. A parallel plate capacitor without a dielectric is charged up so that it stores potential energy U0, and it is then disconnected so that its charge remains the same. A dielectric with constant κ = 2 is then inserted between the plates. What is the new potential energy stored in the capacitor with the dielectric? a) b) c) d)

4U0 2U0 ½ U0 ¼ U0

Physics 259 Final Exam, Winter 2017

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23. Why is the work done on a moving charge by the magnetic force zero? a) b) c) d)

The magnetic force is always perpendicular to instantaneous direction of motion. 󰇍󰇍 does not depend on the path of integration. The integral of∫ 𝐵󰇍 ∙ 𝑑𝑙 A moving charge does not interact with its own magnetic field. The magnetic force is always parallel to instantaneous direction of motion.

24. Which is the correct path for a negative charge travelling from point P with the initial velocity 𝑣 in a uniform electric field?

a) b) c) d)

Path 1 Path 2 Path 3 Path 4

25. The lower loop is connected in a circuit as shown. The upper loop is parallel with the lower loop and right above it. Immediately after the switch is closed, which force will the lower loop exert on the upper loop? a) b) c) d)

a centripetal force an upward force a downward force no force

Physics 259 Final Exam, Winter 2017

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26. Two parallel vertical current carrying wires both have length l = 69.2 cm, are spaced d = 4.62 cm apart, and experience a repulsive force of magnitude 1.35 µN. If the current in wire 1 is I1 = 0.379 A, what is I2? a) b) c) d)

2.38 A up 0.379 A down 0.595 A up 1.19 A down

27. Which integral below correctly gives the electric field strength E at point P on the perpendicular axis of a line of charge of length 2a and uniform linear charge density λ, at a distance x from the line? a  ydy a) E   1 2 2 2  a 2 0 x  y  a

b) E 

a

a

c) E 

a

0

x2  y2

 ydy

1

 4

a

d) E 

xdy

1

 4

0

x

2

a

xdy

1

 4 x 0

 y2 

2

 y2

3/2



3/ 2

28. A current loop is in a uniform magnetic field. Which describes the rotation of the loop? a) The loop tends to rotate so that the direction of the normal vector is in the same direction of the magnetic field vector. b) The loop tends to rotate so that the direction of the normal vector is perpendicular to the direction of the magnetic field vector. c) The loop tends to rotate so that the current is parallel to the direction of the magnetic field vector. d) The loop tends to rotate so that the net force vector on the loop is maximized.

Physics 259 Final Exam, Winter 2017

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29. Two opposite (one positive and one negative) charges have the same mass m, the same magnitude of charge |q| and the same initial velocity 𝑣 at point P. They are undergoing cyclotron motion in a uniform B-field. Which diagram correctly shows the trajectory of the two charges? a) b)

c)

d)

30. In a Hall-effect experiment, a current i = 1.6 A is sent through a 3.2 cm long conductor. The conductor is 0.89 cm wide, and 9.9 µm thick. The current produces a transverse (across the width) Hall potential difference of 9.6 µV when a magnetic field of 1.8 T is passed perpendicularly through the thickness of the conductor. What is the drift speed of the charge carriers? a) b) c) d)

0.63 mm/s 0.42 mm/s 0.54 mm/s 0.87 mm/s

Physics 259 Final Exam, Winter 2017

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31. A solid current carrying wire of an infinite length has a constant current density J and radius R. What is the magnetic field inside the wire a distance r1 from its axis? a) B  µ0 J r21 2 R

b) B 

µ0 J 2r1

c) B  µ0 J r1 2

d) B 

µ0 JR 2 2r1

32. What is the electric field, 𝐸󰇍 at point P due to two charged rods of infinite length, as presented in the figure below? Rod 1 has a positive, linear charge density λ1 and is oriented vertically, a distance d1 from P. Rod 2 has a positive, linear charge density λ2 and is oriented horizontally, a distance d2 from P.

1 𝜆 𝜆 a) 𝐸󰇍 = 2𝜋𝜀 ( 𝑑1 + 2 ) 𝑖

b) 𝐸󰇍 =

c) 𝐸󰇍 = d) 𝐸󰇍 =

1

0

(

1

𝜆1

2𝜋𝜀0 𝑑1 1 𝜆 ( 1 2𝜋𝜀0 𝑑1 1

2𝜋𝜀0

𝜆

𝑗

−

( 𝑑1 𝑗 1

𝑑2 𝜆 − 𝑑2 𝑖) 2 𝜆2

) 𝑖

𝑑2 𝜆 + 𝑑2 𝑖) 2

Physics 259 Final Exam, Winter 2017

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Questions 33, 34 and 35 are all related to the following situation:

In an RC series circuit, ε = 12.0 V, R = 1.39 MΩ, and C = 2.58 µF. 33. What is the time constant? a) b) c) d)

1.668 s 5.82 s 31.2 s 3.59 s

34. What is the maximum charge that will appear on the capacitor during charging? a) b) c) d)

31 µC 25 μC 43 μC 75 μC

35. How long does it take for the charge to build up to 10.0 µC? a) b) c) d)

2.58 s 1.40 s 3.59 s 0.52 s

Physics 259 Final Exam, Winter 2017

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Questions 36, 37 and 38 are all related to the following situation: A long insulated wire carrying current i is bent into a circular section of radius R as shown in the

figure below. Point P is located at the centre of the circular section.

󰇍󰇍󰇍󰇍𝐶 ) 36. In what direction is the magnetic field at point P due to the straight (𝐵󰇍󰇍󰇍𝑆 ) and curved (𝐵 section of the wire? a) b) c) d)

󰇍󰇍󰇍󰇍𝑆 into the page, 𝐵 󰇍󰇍󰇍󰇍𝐶 out of the page 𝐵 󰇍󰇍󰇍󰇍𝑆 is zero, 󰇍󰇍󰇍󰇍 𝐵 𝐵𝐶 into the page 󰇍󰇍󰇍󰇍𝑆 out of the page, 𝐵 󰇍󰇍󰇍󰇍𝐶 out of the page 𝐵 󰇍󰇍󰇍󰇍𝑆 into the page, 𝐵 󰇍󰇍󰇍󰇍𝐶 is zero 𝐵

37. What is the contribution of the wire segment dL to the magnetic field? 󰇍󰇍󰇍󰇍󰇍 = 𝜇0 𝑖𝑑𝐿2 𝑘 a) 𝑑𝐵 4𝜋𝑅 𝜇 𝑖𝑑𝐿 󰇍󰇍 󰇍 󰇍󰇍 b) 𝑑𝐵 = − 0 𝑘 4𝜋𝑅 2

󰇍󰇍󰇍󰇍󰇍 = − 𝜇0 𝑖 𝑘 c) 𝑑𝐵 2𝑅 󰇍󰇍󰇍󰇍󰇍 = 𝜇0 𝑖 𝑘 d) 𝑑𝐵 2𝑅

38. What is the magnitude of the net magnetic field at point P? a) 𝐵 = b) 𝐵 =

𝑅 𝜇0 𝑖

c) 𝐵 = d) 𝐵 =

𝜇0 𝑖

2𝑅 𝜇0 𝑖

2𝑅 𝜇0 𝑖

2𝑅

1

(1 + 𝜋) 1

(1 − ) 𝜋

1

(−1 + 𝜋) 1

(1 + ) 𝜋

Physics 259 Final Exam, Winter 2017

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Questions 39 and 40 are related to the following situation:

The figure below show a toroid with N loops. The inner radius of the toroid’s core is equal to a and the outer radius is equal to b.

39. What is the magnitude of the magnetic field a distance d1 and d3 from the centre of the toroid? a) At d1: 𝐵 =

𝜇𝑜 𝑖𝑁 ; 2𝜋𝑑1

at d3: 𝐵 = 0

𝜇 𝑖𝑁

𝑜 ; b) At d1: 𝐵 = 0; at d3: 𝐵 = 2𝜋𝑑 3

c) At d1: 𝐵 = 𝜇𝑜 𝑖𝑁; at d3: 𝐵 = 0 d) At d1: 𝐵 = 0; at d3: 𝐵 = 0

40. What is the magnitude of the magnetic field a distance d2 from the centre of the toroid (a < d2 < b)? a) 𝐵 = 𝜇𝑜 𝑖𝑁

b) 𝐵 = c) 𝐵 =

𝜇𝑜 𝑖

2𝜋𝑑2 𝜇𝑜 𝑖𝑁 2𝜋𝑑2

d) 𝐵 = 0

Physics 259 Final Exam, Winter 2017

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Questions 41, 42, 43, 44 and 45 are all related to the following situation:

The figure below shows a rectangular loop of wire with length a = 3.4 cm, width b = 1.6 cm placed near an infinitely long wire carrying current i = 4.3 A.

41. Which describes the magnetic field within the loop? a) b) c) d)

It is uniform and directly into the page. It is uniform and directly out of the page. It is nonuniform and directly into the page. It is nonuniform and directly out of the page.

42. What is the correct expression for the infinitesimal area element of the loop you should use to find the magnetic flux through the loop? a) b) c) d)

𝑑𝐴 = 𝑎𝑑𝑟 𝑑𝐴 = 𝑎𝑏 𝑑𝐴 = 𝑎𝑏𝑑𝑟 𝑑𝐴 = 𝑎𝑏𝑟𝑑𝑟

43. What is the flux when the loop is at a distance r from the wire? 𝜇0 𝑖 𝑎𝑏 2𝜋𝑅 𝜇0 𝑖 𝑎𝑟 𝛷𝐵 = 2𝜋𝑅 𝜇 𝑖𝑎 𝑟+0.5𝑏 𝛷𝐵 = 0 ln ( 𝑟−0.5𝑏) 2𝜋 𝜇0 𝑖 𝑟 𝛷𝐵 = 2𝜋𝑎 ln ( 𝑏)

a) 𝛷𝐵 = b) c) d)

Physics 259 Final Exam, Winter 2017

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44. As the loop moves away from the wire with the speed of 0.0022 m/s, the changi...