SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are...

17
Test Version Practice Test Version Practice Test Version Practice Print Name: Instructor: SP212 Spring 2018 Practice Final Exam Exam Rules: 1. You are responsible for these rules. Read them in full. 2. The only electronic device you will be allowed to use during this final exam period is your issue calcu- lator. You are not allowed to borrow another midshipman’s calculator during the exam period. 3. You are not allowed to keep personal items near your desk during the exam period. Please store them at the walls of the room. 4. You are only permitted to look at written materials given to you by your proctor. 5. You have three hours to complete this exam and transfer your answers to the Scantron sheet. Information about filling in the Scantron sheet is on the back of this page. 6. A formula sheet has been provided on the last page. You may remove the last page from this packet during the exam. 7. You may request extra scratch paper from the proctor. You must turn in all used scratch paper with the exam. 8. At the end of the exam, you must turn in all papers. This includes: The exam booklet. The Scantron sheet. Used or unused scratch paper. The formula sheet. If you understand these rules, sign and date below. If not, please ask your proctor for clarification and then sign and date. Signature: Date: Test Version Practice Test Version Practice Test Version Practice

Transcript of SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are...

Page 1: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

Test Version Practice Test Version Practice Test Version Practice

Print Name: Instructor:

SP212 Spring 2018

Practice Final Exam

Exam Rules:

1. You are responsible for these rules. Read them in full.

2. The only electronic device you will be allowed to use during this final exam period is your issue calcu-lator. You are not allowed to borrow another midshipman’s calculator during the exam period.

3. You are not allowed to keep personal items near your desk during the exam period. Please store them atthe walls of the room.

4. You are only permitted to look at written materials given to you by your proctor.

5. You have three hours to complete this exam and transfer your answers to the Scantron sheet. Informationabout filling in the Scantron sheet is on the back of this page.

6. A formula sheet has been provided on the last page. You may remove the last page from this packetduring the exam.

7. You may request extra scratch paper from the proctor. You must turn in all used scratch paper with theexam.

8. At the end of the exam, you must turn in all papers. This includes:

• The exam booklet.

• The Scantron sheet.

• Used or unused scratch paper.

• The formula sheet.

If you understand these rules, sign and date below. If not, please ask your proctor for clarification and thensign and date.

Signature: Date:

Test Version Practice Test Version Practice Test Version Practice

Page 2: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

Test Version Practice Test Version Practice Test Version Practice

Scantron Sheet Checklist

o Pick up a Scantron sheet after you have completed the exam and have indicated your answers on theexam. (Exams will be reviewed manually if necessary as well, so showing your work on it is important.)Remember to circle the best answer to each question.

Then with a soft lead pencil (#2 or HB) completely fill the bubbles, indicating your:

o answers to the 50 exam questions

o alpha code

o section number

o Test Version Practice

o last name

o first initial (F.I.)

o middle initial (M.I.)

In addition, write the following in the provided boxes on the Scantron sheet:

o alpha code

o section number

o last name

o first initial (F.I.)

o middle initial (M.I.)

o your instructor’s last name on the line at the bottom of the sheet

Test Version Practice Test Version Practice Test Version Practice

2

Page 3: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

1. The Sun generates its energy by fusion using the proton-proton chain. The answers represent various possiblefusion reactions in terms of the massive particles created or destroyed (massless particles like neutrinos andphotons have been neglected for simplicity). Each element is represented by its atomic notation in the formAZX where element X has A nucleons and Z protons. There is an error in one of the equations. Which one?

A. 11H + 1

1H −−→ 21H + e+

B. 22He −−→ 2

1H + e+

C. 21H + 1

1H −−→ 32He

D. 32He + 3

2He −−→ 42He + 2

1H

E. 32He + 4

2He −−→ 74Be

Sections Covered: Lesson 1: Chapter 21, Sections 1-3

2. In the picture, there are three unequal charges: q = −15 mC, q1 = +10 mC, and q2 = −25 mC. The chargeq is at coordinates (4 m,0), q1 is at (0, 2 m) and q2 is at (0,−2 m). The angle with respect to the positive xaxis for the net force on q caused by the other two particles is closest to:

x

y

q1

q2

q

A. 0

B. 49.4

C. 17.3

D. −17.3

E. −90

Sections Covered: Lesson 1: Chapter 21, Sections 1-3

3. A positively charged thin wire has a total net charge of q = +20 nC spread uniformly along its length of0.20 m. The wire sits along an x-axis with its left hand tip a distance of d = 0.05 m from the origin, which isrepresented by point P . The electric field at point P from the thin wire is most nearly:

x

y

+ + + + + + +

d L

PA. +14400 i N/C

B. −2880 i N/C

C. +2880 i N/C

D. −14400 i N/C

E. +3400 i N/C

Sections Covered: Lesson 2: Chapter 22, Sections 1-3

4. Two charges, +q and −q form a dipole along the y axis. The direction of the net electric field from thedipole at points P1 and P2 can be described as:

x

y

+ q

− q

+

P2

P1

A. P1 is up and P2 is up.

B. P1 is down and P2 is down.

C. P1 is up and P2 is down.

D. P1 is down and P2 is up.

E. Both will point radially towards the center of the dipole.

Sections Covered: Lesson 3: Chapter 22, Sections 4-5

Page 4: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

5. The figure shows five protons that have been launched in the indicated uniform electric field ~E where themagnitude and direction of the launch velocities are indicated. Rank the protons according to the magnitudeof the accelerations due to the field, greatest first.

A. a = e > b = d > c

B. a = b = c = d = e

C. c > b = d > a = e

D. a > b > c > d > e

E. e > d > c > b > a

Sections Covered: Lesson 4: Chapter 22, Sections 6-7

6. A particular surface is represented by an area vector of ~A = (2i+ 3j + 0k) m2. Calculate the flux Φ1 froman electric field ~E1 = 4i N/C and the flux Φ2 from an electric field ~E2 = 4k N/C through this surface.

A. Φ1 = (8i+ 12j) N·m2/C and Φ2 = (8i+ 12j) N·m2/C

B. Φ1 = −12 N·m2/C and Φ2 = 0 N·m2/C

C. Φ1 = 0 N·m2/C and Φ2 = 8k N·m2/C

D. Φ1 = 12 N·m2/C and Φ2 = −8 N·m2/C

E. Φ1 = 8 N·m2/C and Φ2 = 0 N·m2/C

Sections Covered: Lesson 5: Chapter 23, Sections 1-2

7. Charge is distributed uniformly on the surface of a very large flat conducting plate. The magnitude of theelectric field 0.02 m from the center of the plate is found to be 30 N/C. The magnitude of the electric field0.04 m from the center of the plate is closest to:

A. 7.5 N/C

B. 60 N/C

C. 15 N/C

D. 30 N/C

E. 120 N/C

Sections Covered: Lesson 6: Chapter 23, Sections 3-6

8. The figure shows a spherical shell with a uniform volume charge density of ρ = 1.84 nC/m3, inner radiusa = 0.0930 m and outer radius b = 0.298 m. Calculate the magnitude of the electric field at a distance of0.893 m from the center of the conductor.

A. 2.23 N/C

B. 20.0 N/C

C. 6.80 N/C

D. 0

E. 5.34 N/C

Sections Covered: Lesson 7: Chapter 23, Sections 3-6

4

Page 5: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

9. A particle with mass = 6.7× 10−27 kg and charge = +3.2× 10−19 C moves along the positive x axis with aspeed of 4.8× 105 m/s. It enters a region of uniform electric field parallel to its direction of motion and comesto rest after moving 2.0 m into that field. What is the magnitude of that electric field?

A. 2.0 kN/C

B. 1.5 kN/C

C. 1.2 kN/C

D. 3.5 kN/C

E. 2.4 kN/C

Sections Covered: Lesson 8: Chapter 24, Sections 1-3

10. A particle with a charge q is to be brought from far away to a point near an electric dipole. No workwould be done if the final position of the particle is on:

A. a line through the charges of the dipole.

B. a line that makes an angle of 45o with the dipole moment.

C. a line that makes an angle of 30o with the dipole moment.

D. none of the other options are correct.

E. a line that is perpendicular to the dipole moment.

Sections Covered: Lesson 9: Chapter 24, Sections 4-5

11. Four identical point charges (+50 µC each) have been fixed at the corners of a square of 2.0-m side length.How much external energy is required to bring in a fifth identical charge from infinity to the geometric centerof the square (marked with an ×)?

2 m

+50µC +50µC

+50µC +50µC

×

A. 41 J

B. 16 J

C. 64 J

D. 10 J

E. 80 J

Sections Covered: Lesson 10: Chapter 24, Sections 6-8

12. Does the capacitance of a capacitor increase, decrease, or remain the same when (a) the charge on it isdoubled and (b) when the potential difference across the plates is tripled?

A. (a) same, (b) same

B. (a) increases, (b) increases

C. (a) increases, (b) decreases

D. (a) decreases, (b) increases

E. (a) increases, (b) increases

Sections Covered: Lesson 11: Chapter 25, Sections 1-3

5

Page 6: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

13. How much energy is stored on the 36-µF capacitor in the illustrated circuit, which consists of capacitorsand a single 50 V battery?

50 V

72 µF

36 µF54 µF

A. 50 mJ

B. 2.8 mJ

C. 13 mJ

D. 8.9 mJ

E. 18 mJ

Sections Covered: Lesson 12: Chapter 25, Sections 4-5

14. In the Simple Circuits lab, you built the circuit shown in the figure. What is the formal name of theconcept which states that 1.5 V +VA1 + V22Ω + VA1 = 0 V?

1.5 V 22.0 Ω

A2

A1A. Right Hand Rule

B. EMF Rule

C. Kirchoff’s Junction Rule

D. Kirchoff’s Loop Rule

E. Resistance Rule

Sections Covered: LAB: SIMPLE CIRCUITS

15. A uniform current density of 2.8× 107 A/m2 is directed through a wire with a length of 150 m and aradius of 0.15 mm. The current in the wire is closest to:

A. 0.63 A

B. 26000 A

C. 5.9 A

D. 300 A

E. 2.0 A

Sections Covered: Lesson 13: Chapter 26, Sections 1-3

16. In lecture demo, a negatively charged rubber rod could attract a wood plank if it got close enough. Thereason this happened was:

A. The wood plank was positively charged.

B. Electrical charge if the potential was high enough could cause capacitive breakdown in the air and jump tothe wood, leaving a charge that could be attracted.

C. Polarization in the otherwise neutral wood existed, enough that the negative charges could “push away”the negative sides of the wood atoms while ”attracting” the now closer positive sides.

D. The electric field from the negative charges could attract the neutral wood fibers by inducing a net chargeon them.

E. The wood plank was negatively charged.

Sections Covered: LECTURE DEMO 3: ELECTROSTATICS

6

Page 7: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

17. A rod of length 2.0 m has a square cross section of 2.0 mm × 2.0 mm. It is made from steel which has aresistivity of 6.0× 10−8Ω· m. If a potential difference of 0.50 V is then placed across the ends of the rod, atwhat rate will heat be generated in the rod?

A. 3.0 W

B. 5.3 W

C. 8.3 W

D. 1.3 W

E. 9.3 W

Sections Covered: Lesson 13: Chapter 26, Sections 4-5

18. If the reading on ammeter A is 0.5 A, the value of E is most nearly:

E

12 Ω

12 Ω

A

A. 48 V

B. 12 V

C. 3 V

D. 24 V

E. 6 V

Sections Covered: Lesson 15: Chapter 27, Sections 1

19. The current in the 20 Ω resistor is most nearly:

10 V

10 Ω

15 V

10 Ω

20 Ω

A. 0.75 A

B. 0 A

C. 0.50 A

D. 0.25 A

E. 1.0 A

Sections Covered: Lesson 16: Chapter 27, Sections 2-3

20. There is no energy initially stored on the capacitor. When the switch S is closed, how long will it take forthe capacitor to reach 80 percent of its full energy?

50 V

50.0 Ω

20 mF

S

A. 1.25 s

B. 1.50 s

C. 1.75 s

D. 2.00 s

E. 2.25 s

Sections Covered: Lesson 17: Chapter 27, Section 4

7

Page 8: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

21. An electron moving in the positive x direction experiences a magnetic force in the positive z direction. IfBx = 0, what is the direction of the magnetic field?

A. negative z direction

B. positive z direction

C. positive y direction

D. negative x direction

E. negative y direction

Sections Covered: Lesson 18: Chapter 28, Section 122. The four circuits shown below involve a battery and three capacitors. If C1 = 10 µF, C2 = 20 µF andC3 = 30 µF rank the circuits by their equivalent capacitance, greatest first:

A. a > b > c > d

B. a = b > c = d

C. d > c > b > a

D. a = b = c = d

E. d = c > a > b

Sections Covered: LAB: CAPACITORS

23. What is the kinetic energy of an electron that can pass undeviated through an electric field of 4.0 kV/mwhich is directed perpendicularly to a magnetic field of 8.0 mT? Both fields are perpendicular to the directionof travel of the electron.

A. 1.04× 10−19 J

B. 1.35× 10−19 J

C. 1.14× 10−19 J

D. 8.7× 10−20 J

E. 2.25× 10−19 J

Sections Covered: Lesson 19: Chapter 28, Sections 2-3

8

Page 9: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

24. A charged particle is projected to the left and enters a region with a uniform magnetic field that pointsout of the page. The particle’s trajectory through the region is shown. Which conclusions about the netcharge of the particle and its final speed are correct?

A. The charge is positive and the speed increases.

B. The charge is negative and the speed does not change.

C. The charge is positive and the speed decreases.

D. The charge is negative and the speed increases.

E. The charge is negative and the speed decreases.

Sections Covered: Lesson 20: Chapter 28, Sections 4,6

25. A circular wire coil with 10 loops each of radius 10.0 cm carries a current of 4.00 A. It is placed so thatthe normal to its plane makes an angle of 60 with a uniform magnetic field of 6.00 T. The magnitude of thetorque acting on the loop is closest to:

A. 6.5 N.m

B. 0.65 N.m

C. 3.8 N.m

D. 7.5 N.m

E. 0.75 N.m

Sections Covered: Lesson 21: Chapter 28, Sections 7-8

26. The equivalent resistance for the network of resistors connecting points A and B in the picture is closest to:

3 Ω

3 Ω

6 Ω

BA

A. 11 Ω

B. 1.3 Ω

C. 2 Ω

D. 5 Ω

E. 0.9 Ω

Sections Covered: LAB: KIRCHOFF’S LAWS

27. Three long wires parallel to the x axis carry the indicated currents and directions at the indicated ycoordinates. The magnitude of the magnetic field at the origin is closest to:

y

xO

I1=80 A y1 = 2 m

I2=60 A y2 = −1 m

I3=20 A y3 = −3 m

A. 37 µT

B. 28 µT

C. 19 µT

D. 47 µT

E. 58 µT

Sections Covered: Lesson 22: Chapter 29, Sections 1-2

9

Page 10: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

28. What currents are relevant when performing a calculation using Ampere’s Law?

A. Only currents outside the loop of integration.

B. Only currents parallel to the plane of the loop of integration.

C. Only currents inside the loop of integration.

D. Only currents perpendicular to the loop of integration.

E. Only currents whose magnetic field lines up with the loop of integration.

Sections Covered: Lesson 23: Chapter 29, Section 3

29. Which statement is true about an ideal solenoid?

A. The internal magnetic field is approximately uniform while the external field is weak.

B. The magnetic field is approximately uniform and roughly equal strength both inside and outside thesolenoid.

C. The internal magnetic field strength cannot be calculated using Ampere’s law.

D. The internal magnetic field is weak while the external field is approximately uniform.

E. The internal magnetic field is inversely proportional to the radius of the coils in the solenoid.

Sections Covered: Lesson 24: Chapter 29, Sections 4-5

30. A coil has 300 turns of wire around the perimeter of a circle of radius 0.08 m. A uniform magnetic field isturned on perpendicular to the plane of the coil. This field changes at a constant rate from 20 to 80 mT in atime of 20 ms. What is the magnitude of the induced emf in the coil?

A. 24 V

B. 18 V

C. 15 V

D. 10 V

E. 30 V

Sections Covered: Lesson 25: Chapter 30, Section 1

31. As you saw in lecture demo, when a conducting plate is allowed to swing freely down into a region ofmagnetic field, induced currents (eddy currents) will cause it to:

A. be deflected sideways

B. speed up

C. slow down

D. ”bounce” off the magnetic field

E. be deflected up or down

Sections Covered: MAGNETISM LECTURE DEMO

10

Page 11: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

32. A rod lies across frictionless conducting rails in a constant uniform magnetic field B out of the page asshown. The rod and rails have no intrinsic resistance, but a resistor R has been added to the right side of thecircuit. The magnitude of the force F that must be applied by a person to pull the rod to the left at aconstant speed v is:

A. F = 0

B. F = BLv

C. F =BLv

R

D. F =B2L2v

R

E. F =B2L2v2

R

Sections Covered: Lesson 26: Chapter 30, Sections 2-3

33. A flat coil of wire with 5 turns has a self-inductance of L. The inductance of a similar coil with 20 turnsis:

A. L

B. 4L

C. L/4

D. 16L

E. L/16

Sections Covered: Lesson 27: Chapter 30, Sections 4-5

34. What is the inductance of a series RL circuit in which R = 1000 Ω if the current increases from zero toone-third of its final value in 30µs?

A. 74 mH

B. 99 mH

C. 49 mH

D. 62 mH

E. none of the other options in this list

Sections Covered: Lesson 28: Chapter 30, Section 6

35. After switch S has been closed for a long period of time, the amount of energy stored in the inductor’smagnetic field is closest to:

50 V

50 Ω

20 H

S

A. 0.1 J

B. 5 J

C. 10 J

D. 20 J

E. 50 J

Sections Covered: Lesson 29: Chapter 30, Sections 7-8

11

Page 12: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

36. The figure shows three oscillating LC circuits with identical inductors and capacitors. Rank the circuitsaccording to the period of oscillations, greatest first.

A. c > a > b

B. b > a > c

C. c > b > a

D. a > b > c

E. c > c > a

Sections Covered: Lesson 30: Chapter 31, Section 1-2

37. A capacitor in an LC oscillator experiences a maximum potential difference of 15 V and a maximumenergy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that same instant the potentialdifference across the capacitor is closest to:

A. 5 V

B. 20 V

C. 0 V

D. 15 V

E. 10 V

Sections Covered: Lesson 30: Chapter 31, Section 1-2

38. A 1.0 µF capacitor is connected to an emf that is increasing uniformly with time at a rate of 100 V/s. Thedisplacement current between the plates of the capacitor is:

A. 0 A

B. 1.0× 10−6 A

C. 1.0× 10−4 A

D. 1.0× 10−8 A

E. 100 A

Sections Covered: Lesson 31: Chapter 32, Section 1-3

39. Gauss’ Law for Magnetism,

∮~B · d ~A = 0, tells us:

A. the magnetic field of any current element

B. the net charge in any given volume

C. that currents produce magnetic fields

D. that magnetic monopoles do not exist

E. that the line integral of a magnetic field around any closed loop must vanish

Sections Covered: Lesson 31: Chapter 32, Section 1-3

12

Page 13: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

40. The magnetic field associated with a plane electromagnetic wave is given by the following function where tis in seconds and x is in meters:

~B = 2.6× 10−5 sin(27.2x− 8.17× 109t)z T

The electric field assoicated with this wave is closest to:

A. 2.22× 1011 V/m

B. 3.8× 104 V/m

C. 3.0× 10−8 V/m

D. 7800 V/m

E. 1.28× 10−4 V/m

Sections Covered: Lesson 32: Chapter 33, Sections 1-3

41. A beam of initially unpolarized light is passed through three polarizers, with each transmission axisrotated by 45 clockwise relative to the preceding one. What fraction of the original intensity is transmittedby the set?

A. 0 %

B. 25 %

C. 12.5 %

D. 50 %

E. 33 %

Sections Covered: Lesson 33: Chapter 33, Sections 4-5

42. The figure shows four horizontal layers of different materials with air above and below the stack. Theindex of refraction for each layer is given. Rays of light are sent into the left end of each layer as shown. Inwhich layer is there a possibility of totally trapping the light in that layer so that, after many reflections, all ofthe light reaches the right end of the layer?

A. C only

B. A only

C. D only

D. B only

E. None of them

Sections Covered: Lesson 34: Chapter 33, Section 6-7

13

Page 14: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

43. A concave mirror has a focal length of 20 cm. What is the position of the resulting image if the image isinverted and four times smaller than the object?

A. 15 cm

B. 100 cm

C. 50 cm

D. -15 cm

E. 25 cm

Sections Covered: Lesson 35: Chapter 34, Sections 1-2

44. An object 50 cm high is placed 1 meter in front of a converging lens whose focal length is 1.5 m.Determine the height of the final image.

A. 77 cm

B. 17 cm

C. 52 cm

D. 150 cm

E. 83 cm

Sections Covered: Lesson 36: Chapter 34, Sections 3-4

45. In Young’s double slit experiment, the first order bright fringe occurs because the path difference from thetwo slits is equal to:

A. a fourth of a wavelength

B. a half a wavelength

C. a wavelength

D. three-fourths of a wavelength

E. none of the other answers

Sections Covered: Lesson 37: Chapter 35, Sections 1-2

46. White light reflected from a soap film (n = 1.40) with air on both sides of it appears red (λ = 640 nm).What is the minimum thickness of the film?

A. 124 nm

B. 114 nm

C. 228 nm

D. 134 nm

E. 234 nm

Sections Covered: Lesson 38: Chapter 35, Sections 4-5

14

Page 15: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

47. How wide must a narrow slit be if the first diffraction minimum from laser light of wavelength 633 nmpassed through it occurs at ±12?

A. 3.0× 10−5 m

B. 6.1× 10−6 m

C. 3.0× 10−6 m

D. 6.1× 10−5 m

E. 1.5× 10−6 m

Sections Covered: Lesson 39: Chapter 36, Sections 1,3

48. When you looked through the diffraction grating at the helium tube during lab, the images appeared tobe:

A. a single image only that looked no different than looking at the tube without the grating.

B. many images of the tube, the center one looked the same color but the others were of a variety of colors.

C. many images of the tube, none of which looked like the tube did without the grating.

D. many images of the tube, all looked like the tube did without the grating.

E. a single image that was red, because no other orders were visible.

Sections Covered: LAB: DIFFRACTION GRATING

49. A radar installation operates at 9.0 GHz with an antenna (dish) that is 15 m across. Determine themaximum distance at which this system can distinguish two aircraft that are side by side 100 m apart.

A. 7.4 km

B. 370 km

C. 37 km

D. 3700 m

E. 740 km

Sections Covered: Lesson 40: Chapter 36, Section 5

50. In the final lecture demonstration what was the reason that we prefer parabolic collecting surfaces likeradar dishes rather than spherical shapes?

A. They are easier to shape and coat during construction.

B. Parabolic dishes do not possess a Brewster’s angle for polarization of reflected light like spherical ones do.

C. Spherical surfaces do not focus light arriving far away from the central axis, but parabolic shapes do.

D. Parabolic dishes have a smaller f-number.

E. Spherical dishes have smaller indices of refraction.

Sections Covered: LECTURE DEMO 6, OPTICS

15

Page 16: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

SP212 Spring 2018 Final Exam Equation Sheet, page 1

Prefixes: 103 kilo k , 106 mega M , 109 giga G , 1012 tera T , 1015 peta P

10−3 milli m , 10−6 micro µ , 10−9 nano n , 10−12 pico p , 10−15 femto f

Constants: ε0 = 8.85× 10−12 C2/N·m2 , k = 8.99× 109 N·m2/C2 ,

e = 1.602× 10−19 C , me = 9.109× 10−31 kg , mp = 1.673× 10−27 kg ,

µ0 = 4π × 10−7 T·m/A , c = 3.00× 108 m/s , 1 eV = 1.602× 10−19 J

Geometry: (circle circumference) = 2πr, (circle area) = πr2, (cylinder volume) = πr2h

(sphere area) = 4πr2, (sphere volume) = 43πr

3, arc length formula: s = rθ

Trigonometry: sin θ =opposite

hypotenuse, cos θ =

adjacent

hypotenuse, tan θ =

opposite

adjacent

sin2 θ + cos2 θ = 1, sinα+ sinβ = 2 sin 12 (α+ β) cos 1

2 (α− β), cosα+ cosβ = 2 cos 12 (α+ β) cos 1

2 (α− β)

Vectors: ~A = Ax i +Ay j +Azk, | ~A| = A =√A2x +A2

y +A2z, ~A · ~B = AB cosφ = AxBx +AyBy +AzBz

| ~A× ~B| = AB sinφ, ( ~A× ~B)x = AyBz −AzBy, ( ~A× ~B)y = AzBx −AxBz, ( ~A× ~B)z = AxBy −AyBx

Calculus:d

dx(uv) =

(du

dx

)v + u

(dv

dx

)(product rule),

df

dx=df

du

du

dx(chain rule)

d

dx(xn) = nxn−1,

d

dxex = ex,

d

dx(lnx) =

1

x,

d

dxsinx = cosx,

d

dxcosx = − sinx∫

xn dx =1

n+ 1xn+1,

∫ex dx = ex,

∫dx

x= ln |x|,

∫cosx dx = sinx,

∫sinx dx = − cosx

Coulomb’s Law and Electric Charge: k =1

4πε0, ~FE = k

q1q2r2

r, q = ne, n = 0,±1,±2, ...

Electric Fields: ~E =~FEq0

, ~E = kq

r2r , d ~E(~r) = k

dq

r2r,

dq = λds , dq = σdA , dq = ρdV , ~FE = q ~E , ~p = q~d , ~τ = ~p× ~E , U = −~p · ~E

Gauss’ Law: ΦE =

∮~E · d ~A =

qencε0

, E =σ

ε0, E =

λ

2πε0r, E =

σ

2ε0

Electric Potential: ∆V =∆U

q, Vf − Vi = −

∫ f

i

~E · d~s , V = kq

r, V = k

∫dq

r,

Es = −∂V∂s

, Ex = −∂V∂x

, Ey = −∂V∂y

, Ez = −∂V∂z

, U = kq1q2r

Capacitance: q = CV , C =κε0A

d, Ceq =

n∑i=1

Ci (parallel) ,

1

Ceq=

n∑i=1

1

Ci(series) , U =

q2

2C=

1

2CV 2 , u =

1

2ε0E

2

Current and Resistance: i =dq

dt, i =

∫~J · d ~A , i = nAevd , ~J = (ne)~vd , ~E = ρ ~J ,

R = ρL

A, R =

V

i, ρ− ρ0 = ρ0α(T − T0) , P = iV = i2R =

V 2

R

16

Page 17: SP212 Spring 2018 Practice Final Exam...SP212 Spring 2018 Practice Final Exam Exam Rules: 1.You are responsible for these rules. Read them in full. 2.The only electronic device you

SP212 Spring 2018 Final Exam Equation Sheet, page 2

Circuits: E =dW

dq, Pemf = iE , V = E − ir, Req =

n∑i=1

Ri (series) ,1

Req=

n∑i=1

1

Ri(parallel) ,

τC = RC , q = CE(1− e−t/τC

), i =

dq

dt=

(E

R

)e−t/τC , VC = E

(1− e−t/τC

),

q = q0e−t/τC , i =

dq

dt= −

( q0RC

)e−t/τC

Magnetic Fields: ~FB = q~v × ~B , |q|vB =mv2

r, ω =

T= 2πf =

|q|Bm

,

~FB = i~L× ~B , d~FB = id~L× ~B , ~µ = Ni ~A , ~τ = ~µ× ~B , U = −~µ · ~B

Magnetic Fields Due to Currents: d ~B =µ0

i(d~s× r)r2

, Bline =µ0i

2πR, Barc =

µ0iφ

4πR, Fba =

µ0Liaib2πd

,∮~B · d~s = µ0ienc , Bsolenoid = µ0in , n = N/L , Btoroid =

µ0iN

1

r, Bloop(z) =

µ0iR2

2(R2 + z2)3/2

Induction and Inductance: ΦB =

∫~B · d ~A , E = −N dΦB

dt, E =

∮~E · d~s , E = BLv , L =

NΦBi

,

L

l= µ0n

2A , EL = −Ldidt

, τL = L/R , i =E

R

(1− e−t/τL

), i = i0e

−t/τL , UB =1

2Li2 , uB =

B2

2µ0

Electromagnetic Oscillations: q = Q cos(ωt+ φ) , ω =1√LC

, i = −ωQ sin(ωt+ φ)

q = Qe−Rt/2L cos(ω′t+ φ) , ω′ =√ω2 − (R/2L)2

Maxwell’s Equations: ΦE =

∮~E · d ~A =

qencε0

, ΦB =

∮~B · d ~A = 0 ,

∮~E · d~s = −dΦB

dt,∮

~B · d~s = µ0id,enc + µ0ienc, id = ε0dΦEdt

Electromagnetic Waves: E = Em sin(kx− ωt) , B = Bm sin(kx− ωt)

c =E

B=

1√µ0ε0

, c = λf =ω

k, ω = 2πf , k =

λ,

~S =1

µ0

~E × ~B, Savg = I =1

cµ0E2

rms , Erms =Em√

2, I =

PS4πr2

, pr =I

c, pr =

2I

c,

I =1

2I0 , I = I0 cos2 θ, n =

c

v, n2 sin(θ2) = n1 sin(θ1) , θc = sin−1

n2n1

, θB = tan−1n2n1

Images (Mirrors and Lenses): i = −p, 1

p+

1

i=

1

f=

2

r,

n1p

+n2i

=n2 − n1

r,

1

p+

1

i=

1

f= (n− 1)

(1

r1− 1

r2

), m = − i

p, |m| = h′

h

Interference: λn =λ

n, d sin θ = mλ, m = 0, 1, 2, ... , d sin θ =

(m+

1

2

)λ, m = 0, 1, 2, ...

2L =

(m+

1

2

n2, m = 0, 1, 2, ... , 2L = m

λ

n2, m = 0, 1, 2, ..

Diffraction: a sin(θ) = mλ, m = 1, 2, 3, ... , sin θ = 1.22λ

d, θR = 1.22

λ

d, d sin θ = mλ, m = 0, 1, 2, ...

17