LE1 AY14-15 1S

University of the PhilippinesCollege of Science

Physics 72

Set AFirst Long Exam

First Semester, AY 2014–2015

Name: Instructor:

Section/Class Schedule: Student Number:

Course: College:

First Long Exam First Semester, AY 2014–2015 Physics 72

INSTRUCTIONS: Choose the best answer and shade the corresponding circle on your answersheet. To change your answer, cross-out and sign your original answer and then shade yournew answer. No computational devices allowed (e.g. calculators, mobile phones). Any formof 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:

Area VolumeSphere (radius=r) 4πr2 4

3πr3

Cylinder (radius=r, height=h) 2πr2 + 2πrh πr2h

sin(π/3) = cos(π/6) =√

3/2cos(π/3) = sin(π/6) = 1/2sin(π/4) = cos(π/4) =

√2/2

Useful constants:

e −1.60× 10−19 Cme 9.1× 10−31 kgε0 8.854× 10−12 C2/Nm2

k 8.988× 109 Nm2/C2

1. Electric Field. Given the charges +Q and −2Q, which of the following diagrams shows acorrect representation of the electric field lines?

A.B.

C.

D.

E.

2. Coulomb Force. What is the net Coulomb force oncharge +Q3 due to the other two identical charges +Qas shown in the figure?

A. kQQ3

s2 (1 +√22 )ı− kQQ3

s2

√22

B. kQQ3

s2 (1 +√22 )ı+ kQQ3

s2

√22

C. 2kQQ3

s2 ı− kQQ3

s2

D. kQQ3

s2 ı+ kQQ3

s2

E. kQQ3

s2 (1 +√24 )ı− kQQ3

s2

√24

A – 2


3. Die Paul, die! Which of the following is a correct de-scription of the motion of the dipole immersed in a uni-form electric field as shown in the figure?

A. It will rotate clockwise.

B. It will rotate counterclockwise.

C. It is static but unstable

D. It is static and stable.

E. It will move to the right.

4. Electric Failed Lines. Consider the electricfield lines shown in the figure. Which of thefollowing is true about the charges P , Q, andR?

A. P , Q, and R are all negative

B. P = Q = R

C. Q < 0, 0 < P < R

D. Q < 0, P = R > 0

E. P , Q, and R are all positive

5. Saan? A +2q point charge at (−a, 0) produces an elec-tric field E1 at point P. Where must a +q point chargebe located along the x-axis so that the magnitude of itselectric field E2 at point P is equal to E1?

A. (a, 0)

B. (√

2a, 0)

C. (−a/2, 0)

D. (0, 0)

E. (a/2, 0)

A – 3


6. Dipole on a uniform electric field. A dipole is placedalong the x-axis as shown. Which of the following elec-tric field(s) will give the minimum potential energy?

I. E = E0ı

II. E = −E0ı

III. E = E0

A. I onlyB. II onlyC. III only

D. I and II only

E. I and III only

7. Coaxial Cable. Two very long coaxial cylindrical shells have radii a < b as shown. Theinner shell has a uniform linear charge density +λ while the outer shell has no net charge.Let Ebet be the electric field at the region between the cylinders (a < r < b) and Eout bethe electric field at the outermost region (r > b). Which of the following is true about themagnitudes of the electric fields?

A. Ebet < Eout

B. Ebet = Eout > 0

C. Ebet > Eout

D. Ebet = Eout = 0

E. Ebet = 0, Eout > 0

8. Conducting Sphere & Shell. Consider a solid sphereinside a spherical conducting shell as shown. The solidsphere has charge +4Q and the spherical shell has charge+5Q. What is the electric field in the region between thesphere and shell?

A. 0

B. kQ/r2

C. +4kQ/r2

D. +5kQ/r2

E. +9kQ/r2

A – 4


9. Rotating E-field. Consider a sheet of area A with normal vectorn as shown. It is placed in a uniform electric field of magnitudeE. Which of the following is the correct relationship of the electricflux through the sheet if the electric field is rotated in three differentdirections I, II and III?

A. I > II > III

B. I > III > II

C. III = I > II

D. III > I = II

E. I = II = III

For the next two items, consider five point charges enclosedby five different surfaces I, II, III, IV and V where Q > 0.

10. Flux of my heart. What is the electric flux through sur-face II?

A. 2Q/ε0

B. Q/ε0

C. zero

D. −Q/ε0

E. −2Q/ε0

11. Largest flux. Which surface has the largest electric flux?

A. I B. II C. III D. IV E. V

12. Bear flux. Consider a charged bear of irregular shape enclosed by a Gaussian sphere ofradius R. Which of the following statement(s) is/are true?

I. Gauss’ law cannot be used to calculate the electric flux through the surface of thesphere.

II. The electric flux through the sphere is smaller when the bear is moved a distance R/4from the center but still inside the sphere.

III. The electric flux through the sphere is proportional to the charge of the bear.


D. I and II only

E. II and III only

A – 5


13. Dipole inside. A dipole with charges of magnitude 2 nC is placed inside the cavity of asolid conductor. The solid conductor has a net charge of +5 nC. What is the total chargeat the outer surface of the conductor?

A. +1 nC B. +2 nC C. +3 nC D. +4 nC E. +5 nC

For the next two items, consider the equipotential curves forthe point charges q1 and q2 as shown.

14. Charge Nature. What is the nature of the charges?A. |q1| < |q2|, same signs

B. |q1| = |q2|, same signs

C. |q1| > |q2|, same signs

D. |q1| < |q2|, opposite signs

E. |q1| = |q2|, opposite signs

15. EField. Which of the following is the correct electric field vector at point P ?

A. ↑ B. ↓ C. ← D. → E.

16. Potential Gradient. Consider the potential V (x, y, z) = A + Bx − Cxy2z3 at a certainregion in space where A, B, and C are constants. Which of the following is the electricfield E(x, y, z)?

A. E = (Bx+ Cxy2z3)ı+ (Cxy2z3)+ (Cxy2z3)k

B. E = −(Bx− Cxy2z3)ı− (−Cxy2z3)− (−Cxy2z3)k

C. E = (Bx− Cxy2z3)ı+ (−Cxy2z3)+ (−Cxy2z3)k

D. E = −(B − Cy2z3)ı− (−2Cxyz3)− (−3Cxy2z2)k

E. E = (B − Cy2z3)ı+ (−2Cxyz3)+ (−3Cxy2z2)k

A – 6


17. Equipotential. Consider the spherical equipotential sur-faces of a positive point charge as shown in the fig-ure. The potential difference between the surfaces ismeasured to be 2.00 V. Another positive test chargeq = 1.00 nC is brought from A to C, and then to B. Whatis the total work done by the electric field in moving thetest charge?

A. 2.00 nJ

B. 1.00 nJ

C. zero

D. −1.00 nJ

E. −2.00 nJ

18. Paths. Consider an electron moving along one of thethree paths shown. The correct increasing order of thework done by the electric field on the electron is

A. 2, 3, 1

B. 3, 1, 2

C. 2, 1, 3

D. 1, 2, 3

E. 1, 3, 2

19. 4charge. Four identical point charges with charge +qare placed at the corners of a square as shown. What isthe electric potential at the center of the square P?

A. 4kqd

B. 2√2kqd

C. zero

D. −2√2kqd

E. −4kqd

A – 7


20. Solid. Consider a solid spherical conductor with radius R andcharge −Q at electrostatic equilibrium. What is the correct rank-ing of the Points A, B, C and D according to the values of theirelectric potential?

A. A = B < C = D

B. A = B > C > D

C. A = B < C < D

D. A > B > C = D

E. A < B < C < D

21. Dielectric. Consider an isolated capacitor with initial charge Q. Which of the followingis/are true about the effect of inserting an uncharged dielectric between conducting plates?

I. The magnitude of charge on each plate remains the same.

II. The capacitance decreases.

III. The electric field between the plates decreases.


D. I and III only

E. II and III only

22. Capacitor Network. What is the equivalent capacitance ofthe capacitor network shown in the figure?

A. 73C

B. 37C

C. 65C

D. 56C

E. 5C

A – 8


23. Potential Difference. What is the potential differencebetween points A and B in the circuit shown?

A. 0

B. 13V

C. 12V

D. 23V

E. V

24. Connected Capacitors. Two initially uncharged capacitors withcapacitance C and 3C are connected to a constant voltage sourceV as shown in the figure. What is the total stored energy in bothcapacitors at equilibrium?

A. 12CV

2

B. CV 2

C. 32CV

2

D. 2CV 2

E. 4CV 2

25. Compressed Plates. A parallel plate capacitor consists of conducting plates with equalareas, separated by some distance D. The capacitor is connected to a constant voltagesource. Which of the following statements is/are true if we decrease the separation distancebetween the capacitor plates, while it is connected to the voltage source?

I. The capacitance will decrease.

II. The stored charge will increase.

III. The stored energy will stay the same.


D. I and II only

E. II and III only

A – 9


For the next two items, consider a parallel plate capacitor with a capacitance of 10 mF andcharge density σ. The separation distance between the plates is 10 mm. A potential differenceof 500 V is applied across the capacitor.

26. Area . What is the area of each plate (in terms of ε0)?

A. 1ε0

(1× 10−4) m2

B. 1ε0

(1× 10−5) m2

C. ε0(1× 10−4) m2

D. ε0(1× 10−5) m2

E. 1ε0

(1× 10−6) m2

27. What the E.F. What is the electric field magnitude between the plates?

A. 500 kV/m

B. 50 kV/m

C. 0.02 kV/m

D. 0.2 kV/m

E. 100 kV/m

28. Hatit-Taas. A conductor has resistivity ρ, length L, radius r and resistance R. Which ofthe following changes on the conductor will reduce its resistance by 1/4?

I. Double both the resistivity and radius.

II. Halve the length and double the radius.

III. Double the radius.


D. I and II only

E. II and III only

29. Curly Tops. Which of the following statements is/are TRUE about the I-V curve of anOhmic material?

I. The plot is exponentially increasing.

II. The plot is linearly increasing.

III. The plot is linearly decreasing.


D. I and II only

E. II and III only

A – 10


For the next two items, consider a 10.0 Ω resistor connected to a power supply of unknownvoltage and without internal resistance.

30. Ipaglaban Mo. If a 1.50 A current flows through the resistor, what is the voltage acrossthe resistor?

A. 7.50 V

B. 15.0 V

C. 22.5 V

D. 30.0 V

E. 45.0 V

31. Vary-Vary. If the resistance is doubled, what will happen to the power dissipated?

A. QuarteredB. QuadrupledC. Halved

D. Doubled

E. Remains constant

32. Omega Rho. The resistivity of Metal X was found to increase linearly by 20% (ρ1/ρ0 =1.20) as its temperature increases from T0 to T1. Given a piece of wire made of pure MetalX, if its dimensions and the voltage across it are kept constant, what fraction of the currentI0 at temperature T0 remains after the temperature is increased to T1?

A. I1 = 16I0

B. I1 = 56I0

C. I1 = 15I0

D. I1 = 45I0

E. I1 = 65I0

33. Current density. Given a system of n positive charges moving in a wire with diameter D,drift velocity vd, and current density J. Which of the following is the drift velocity of asystem moving in a wire with diameter 1

2D having the same magnitude of J?

A.1

4vd

B. −1

4vd

C. 4vd

D. −4vd

E. vd

A – 11


For the next four items, consider the circuitshown. Each resistor has the same resistance1.0 Ω.

34. Requivalent. What is the equivalent resistance of the circuit?

A.3

7Ω

B.5

6Ω

C.1

2Ω

D.6

4Ω

E.7

3Ω

35. Current. Which of the following is true about the current passing through each resistorwhen an ideal battery of voltage 2 V is connected to the circuit?

A. I1 > I2 > I3B. I3 > I4 > I5

C. I1 = I2 < I3D. I3 = I4 < I5

E. I3 = I4 = I5

36. Current din. If the potential difference between a and b is 2 V, what is the current throughR1?

A. 1 A B. 2 A C. 3 A D. 4 A E. 5 A

37. Voltage. If the potential difference between a and b is 2 V, what is the voltage across R1?

A. 5 V B. 4 V C. 3 V D. 2 V E. 1 V

38. RC. Consider a circuit composed of a fully-charged capacitor C and a resistor R. Whichof the following statement(s) is/are true after the circuit is left for a very long time?

I. The current through R approaches zero.

II. The charge of C approaches its maximum value.

III. The power dissipated by R approaches its maximum value.

A. I onlyB. II onlyC. I and II only

D. II and III only

E. I, II and III

A – 12


For the next two items, consider the following circuit diagram. It is composed of three 1 Ωresistors and two power supplies with 2 V and 10 V potential differences. Using the specifiedcurrent directions, solve the following:

39. I2. What is the current passing through R1?

A. −2.0 A

B. +2.0 A

C. +1.0 A

D. +0.5 A

E. −0.5 A

40. I1. What is the current passing through R2?

A. 2.0 A

B. −2.0 A

C. +4.0 A

D. −4.0 A

E. 6.0 A

A – 13

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LE1 AY14-15 1S