Physics 72 Samplex

University of the Philippines College of Science

Physics 72 Set A Second Long Exam Second Semester, AY 2013–2014

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Second Long Exam

Second Semester, AY 2013–2014

Physics 72

INSTRUCTIONS: Choose the best answer and shade the corresponding circle on your answer sheet. To change your answer, cross-out and sign your original answer and then shade your new answer. No computational devices allowed (e.g. calculators, mobile phones). Any form of cheating in examinations or any act of dishonesty in relation to studies, such as plagiarism, shall be subject to disciplinary action. Following instructions is part of the exam. Useful formulas:

Useful constants:

Area Volume 4 2 3 Sphere (radius=r) 4πr 3 πr Cylinder (radius=r, height=h) 2πr2 + 2πrh πr2 h √ sin(π/3) = cos(π/6) = 3/2 cos(π/3) = sin(π/6) = 1/2 √ sin(π/4) = cos(π/4) = 2/2

e me 0 k

−1.60 × 10−19 C 9.1 × 10−31 kg 8.854 × 10−12 C2 /Nm2 8.988 × 109 Nm2 /C2

1. Broken magnet. A bar magnet with orientation of North (N) and South (S) poles as shown is cut into three pieces. The W pole of the middle piece ATTRACTS the Z pole of another bar magnet. What is the polarity of the X and Y poles? A. X: North, Y: North B. X: North, Y: South C. X: South, Y: North D. X: South, Y: South E. Cannot be determined 2. Magnetic force. An electron initially moving upward encounters a region with uniform magnetic field B with direction shown. Which of the following situations will produce a magnetic force directed INTO THE PAGE? A. I only B. II only C. III only D. I and II only E. I, II and III

A–2

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Physics 72

3. What motion? Charge X is in a region of uniform magnetic field while charge Y is separately in a region of uniform electric field. If both charges are initially held at rest, which of the following best describes the motion of the charges after they are released? (Neglect gravitational effects) A. Only charge X accelerates B. Only charge Y accelerates C. Both charges accelerate

D. Neither of the charges accelerates E. X will change direction, Y will accelerate

4. Parallel. A positive charge moving with initial velocity v in a uniform magnetic field B experiences a magnetic force F. Which of the following statements is/are ALWAYS TRUE? I. v has no component parallel to F. II. B has no component parallel to v. III. F has no component parallel to B. A. I only B. II only

C. II and III only D. I and III only

E. I, II and III

5. Field line. In the figure shown, a bar magnet is placed in the xy-plane with its longer side parallel to the x-axis. What is the direction of the magnetic field at point P due to the bar magnet? A. ˆi

B. −ˆi

C. ˆj

6. Flux. A magnetic field B enters a loop of area A as shown in the figure. What must be the value of θ such that the magnetic flux through the loop is 12 BA? A. 30◦

C. 60◦

B. 45◦

D. 0◦

E. 90◦

A–3

D. −ˆj

ˆ E. k

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7. Zorro. A wire, bent as shown is immersed in a uniform magnetic field B = 1 T directed to the right. The√horizontal segments are 1 m long while the diagonal segment is 2 m long. Current I = 1 A flows in the direction shown. What is the net force on the wire? D. 3 N, into the page

A. Zero B. 1 N, into the page C. 1 N, out of the page

E. 3 N, out of the page

8. Rainbow. Figure shows the path of three positively charged particles as they enter a region of uniform magnetic field directed out of the page. The particles have the same initial speed and have the same masses. Which of the following is the correct relationship between the charge magnitudes Q of the particles? D. QI > QII < QIII

A. QI = QII = QIII B. QI > QII > QIII C. QI < QII < QIII

E. QI < QII > QIII

9. Magnetic field due to point particle. Shown in the figure is the instantaneous position of an electron with velocity v. What is the magnitude and direction of the magnetic field at point P? A. B. C.

µ0 ev 8π r2 , outward √ µ0 3 ev 8π r2 , inward µ0 ev 8π r2 , inward

D.

√ µ0 3 ev 8π r2 ,

E.

µ0 ev 4π r2 ,

outward

inward

A–4

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10. B due to infinitesimal current. What is the magnetic field at point (a, a) due to the two identical current elements of infinitesimal length ∆L as shown in the figure? A.

µ0 I∆L ˆ 4π a2 k

D.

µ0 I∆L ˆ 2π a2 k

B. zero µ0 I∆L ˆ C. − 4π a2 k

µ0 I∆L ˆ E. − 2π a2 k

11. Two infinite straight wires. What is the magnetic field at point P due to the two infinite straight wires with current directed into the page as shown in the figure? A.

√ µ0 2 I ı 2π r ˆ

B. C.

√ µ0 2 I ˆ 2π r  µ0 I ı π rˆ

D. − µπ0 Ir ˆı E.

µ0 I ˆ 4π r 

12. B due to a loop. What is the magnetic field at the origin (0, 0) due to the current loop shown in the figure? A. B. C.

µ0 I 1 2 (b µ0 I 1 8 (a µ0 I 1 2 (a

ˆ − a1 )k

D. zero

ˆ − 1b )k

E.

µ0 I 1 8 (b

ˆ − a1 )k

ˆ − 1b )k

13. vanishing force. Shown in the figure are three infinite straight wires with the indicated currents. Which of the wires will experience a vanishing force per unit length? A. 1 only

C. 3 only

B. 2 only

D. 1 and 3

E. 2 and 3

A–5

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Physics 72

14. proton. A proton with charge e has a velocity v = vxˆı +vy ˆ. At the instant when the proton is at the origin (x, y, z) = (0, 0, 0), which of the following gives the correct magnetic field at point (x,y,0)? √ √ ˆ µ0 e (vx − vy ) ˆ ˆ 2 vz ˆ µ e µ0 e 2 (vx i − vy j) 0 A. k D. k C. 4π x2 + y 2 8π x2 + y 2 8π x2 + y 2 µ0 e (vx y − vy x) ˆ µ0 e vz ˆ B. k E. k 4π (x2 + y 2 )3/2 4π x2 + y 2

For the next two numbers, consider an infinitely long solid cylinder cylinder (radius a) coaxial but insulated with a hollow, infinitely long cylinder (inner radius b, outer radius c). Equal currents I flow across the cylinders, into the page as shown. 15. Middle. What is the magnitude of the magnetic field at the space between the conductors (a < r < b)? A. Zero

C. µ◦ I/(3πr)

B. µ◦ I/(πr)

D. µ◦ I/(2πr)

E. µ◦ Ir/(2πb2 )

16. Outside. What is the magnitude of the magnetic field outside the conductors (r > c)? A. Zero B. µ◦ I/(πr)

C. µ◦ I/(3πr) D. µ◦ I/(2πr)

E. µ◦ Ir/(2πb2 )

17. Together. A pair of electrons a distance d apart lies in the x-axis. They move with identical speed v in the +x direction. What is the magnetic field midway between the two electrons? A. Zero B.

µ0 ev ˆ 4π d2 k

µ0 ev ˆ C. − 4π d2 k D. µ0 ev2 ˆj 4π d

A–6

µ0 ev ˆ E. − 4π d2 j

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Physics 72

18. Lenz’ Law. Consider a loop lying in the xy-plane and immersed in a region of spatially uniform magnetic field whose magnitude is either increasing or decreasing. Which of the following correctly depicts the direction of the induced current in the loop?

A.

C.

B.

D.

E.

19. New emf. A metal ring is oriented with the plane of its area perpendicular to a spatially uniform magnetic field that increases at a steady rate. If the radius R of the ring is halved, by what factor does the induced emf in the ring change? A.

1 2

B.

1 4

C. 2

D. 4

E. 1

20. CW . Consider a conducting loop whose axis coincides with that of a bar magnet. In case 1, the loop moves downward with its plane still perpendicular to the axis of the magnet. In case 2, on the other hand, the bar magnet moves downward along the axis of the loop. What must be P , Q, X and Y so that in both cases a current is induced in the clockwise direction as seen from above the loop? A. P : South, Q: North, X: North, Y : South B. P : North, Q: South, X: South, Y : North C. P : South, Q: North, X: South, Y : North D. P : North, Q: South, X: North, Y : South E. P : South, Q: South, X: North, Y : North

A–7

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Physics 72

21. Rectangular coil. A rectangular coil with area 1 m2 and oriented in the horizontal xyplane is located in a region of uniform magnetic field that varies with time according to B(t) = (1 T/s2 )t2 . The magnetic field is at an angle of 30◦ with the plane of the coil. What is the magnitude of the induced emf in the coil at time t = 1 s? √

A. 1 V √ B. 3 V

D.

C. 2 V

E. zero

3 2

V

22. Rectangle +Wire. A metal rectangle is close to a long, straight, current-carrying wire, with two of its sides parallel to the wire as shown in the figure. Which of the following is/are TRUE? I. If the rectangle is moved downward, there is NO induced current in the rectangle. II. If the current in the long wire is decreasing, there is an induced current in the rectangle in the clockwise direction. III. If the rectangle is moved to the left, there is an induced current in the rectangle in the counterclockwise direction. A. I only

D. I and II only

B. II only C. III only

E. I and III only

A–8

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Physics 72

23. Max emf. A bar of length 1 m moves through a uniform magnetic field with magnitude 1 T with speed 1 m/s. In which direction should this bar move so that the emf across its ends is maximum? A. 1 or 2 B. 3 or 4 C. x- or −x-direction D. y- or −y-direction E. z- or −z-direction

24. Function. Given an electric field described by the function E(t) = 0.15 N/C sin 2t where t is in seconds, what is the MAXIMUM displacement current through a 1 m2 area perpendicular to E? C. 0.0750 D. 0.60

A. zero B. 0.30

E. 0.150

25. E-induced. A circular loop with radius of 0.1 m, is placed in a time varying magnetic field as shown in the figure. If the magnitude of the magnetic field increases at a rate of 0.20 T/s, what is the magnitude of the induced electric field in the loop? A. 0.01 V/m

C. 0.10 V/m

B. 0.02 V/m

D. 0.20 V/m

E. 0.001 V/m

26. Injuiced. Two loops have mutual inductance of 5 mH. A constant current of 5 A is present in one of the coils. What is the induced emf on the other coil? A. 25 mV B. 10 mV

C. 5 V D. 1 mV

E. Zero

27. Critical. If R = 1.0 Ω and L = 2.0 µH,what value of capacitance C will make an L-R-C series circuit critically damped? A. 0.5 µF

B. 1.0 µF

C. 2.0 µF

A–9

D. 4.0 µF

E. 8.0 µF

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Physics 72

28. Giant. A giant coil has an area of 8 m2 and 16 m in length. How many turns would create a self-inductance of 2 H? A.

√4 µ0

B.

√8 µ0

C.

√6 µ0

D.

√2 µ0

E.

√16 µ0

29. Energy Catcher. A certain region in space contains a magnetic field of 0.2T. You place a cubical box of side length 2m2 to catch some energy. What is the magnetic energy density inside the box? A.

0.08 µ◦

B.

0.16 µ◦

C.

0.02 µ◦

D.

0.004 µ◦

E.

0.1 µ◦

For the next three numbers, consider An LC Circuit containing a 5H inductor and a 5F capacitor. The current oscillates with amplitude of 2A. 30. Max Out! What is the maximum charge on the capacitor? A. 1.0C

B. 7.5C

C. 5C

D. 2.5C

E. 10.0C

31. Repeat. What is the oscillation frequency of the circuit? A. 0.1rad/s B. 0.2rad/s

C. 0.25rad/s D. 0.5rad/s

E. 0.75rad/s

32. Start. If the capacitor has maximum charge at time t = 0, then what is the energy stored in the inductor at t = 0? A. 0.01J

B. 0.02J

C. 0.05J

D. Zero

E. 0.20J

For the next two numbers consider the phasor diagram. The values of resistance R, capacitive reactance XC , and inductive reactance XL of three circuits are given in the table.

33. Matching type. Which of the circuits match/es the phasor diagram? A. I only B. II only

C. III only D. II and III only A – 10

E. I and III only

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Physics 72

34. Zzzzz. What is the impedance of circuit II? A. 9 kΩ

B. 7 kΩ

C. 3 kΩ

D. 25 kΩ

E. 5 kΩ

35. Insta-avenue. Consider an RLC series circuit driven by an AC source with fixed voltage amplitude. If the driving frequency is ω1 , the phase angle is −10◦ . If the driving frequency is ω2 , the phase angle is +10◦ . Which of the following is/are true? I. The instantaneous power at any given time t is equal for the two frequencies. II. The average power is equal for the two frequencies. III. The rms current is the same for both frequencies. A. I only B. II only

C. III only D. II and III only

E. I, II, and III

36. phasensyahan. Consider three independent LRC series circuits. At a driving frequency ω, the phase angles for circuits I, II, and III are −30◦ , +30◦ , and +60◦ , respectively. If the resistance are the same for all three circuits, which of the following best describes the impedance? A. I = II < III B. I = II > III

C. I < II < III D. I > II > III

E. I = II = III

For the next two questions, consider three different LRC circuits connected to an AC source with the same peak amplitude. All inductors and capacitors are ideal and the values of the resistance R, inductance L, and capacitance C are given in the table. 37. At resonance. Which of the following correctly describes the maximum current in the circuit at resonance? A. I=II
C. I=II=III D. I=III>II

E. I=II>III

38. Circuit II. If the amplitude of the AC source is 5.0 V and the frequency is 10, 000 rad/s what is the average power dissipated in the resistor for circuit II?

A – 11

Second Long Exam

A. 1/50 W B. 1/32 W


C. 1/40 W D. 1/25 W

Physics 72

E. 1/16 W

39. Bagay! Figure shows the current versus time plot of an ideal AC source and the voltage versus time plot of a resistor, ideal inductor, and ideal capacitor when they are connected separately to the source. Which of the following correctly matches the circuit element to its corresponding voltage versus time plot?

A. X-Inductor, Y- Capacitor, Z-Resistor B. X-Resistor, Y- Inductor, Z-Capacitor C. X-Capacitor, Y- Resistor, Z-Inductor D. X-Inductor, Y- Resistor, Z-Capacitor E. X-Resistor, Y- Capacitor, Z-Inductor 40. Root. A 12.0 Ω resistor is connected across a sinusoidal emf that has a peak value of 48.0 V. What is the rms value of the current passing through the circuit? √ 2 D. 4 A B. 2 2A A. √ A √ 2 C. 2 A E. 4 2 A

A – 12

Physics 72 Samplex

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