University of the Philippines College of Science PHYSICS 72 Summer 2012-2013 Second Long Problem Set
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). Following instructions is part of the exam. Useful formulas: Area Volume 4 Sphere (radius = r) 4πr 2 3 πr3 Cylinder (radius =r, height = h) 2πrh πr 2 h Useful constants: e -1.60 x 10-19 C m e 9.1 x 10-31 kg ε o 8.854 x 10-12 C 2 /Nm 2 k 8.988 x 10 9 Nm 2 /C 2 θ 0 π/6 π/3 π/4 π/2 sin θ 0 1 3 2 1 2 2 2 cos θ 1 3 1 2 0 2 2 2 tan θ 0 1 3 3 1 For the next two numbers, consider a positive charge (+Q) moving counterclockwise at constant velocity as shown in the figure. The region has a uniform external magnetic field. 1. Bee. What is the direction of the external magnetic field experienced by the charge? A. Towards + x-axis B. Towards x-axis C. Towards +y-axis D. Out of the page E. Into the page 2. Mass effect. If the mass of the charge is doubled, how would this change its motion? A. It will move counterclockwise, but at a larger radius B. It will move counterclockwise, but at a smaller radius C. It will move clockwise at a larger radius D. It will move clockwise at a smaller radius E. It will move clockwise the same radius For the next two numbers, consider a circular coil with diameter of 4m and has a clockwise current I = 1 A in the x-y plane. A uniform magnetic region B = 2T is then set up along positive z-axis. 3. Moments. What is the magnitude and direction of the coil s magnetic moment as drawn in the figure? A. µ = 4 A.m 2 ; towards +x B. µ = 4 A.m 2 ; towards z C. µ = 4 A.m 2 ; towards +z D. µ = 4π A.m 2 ; towards z 1
E. µ = 4π A.m 2 ; towards +z 4. Force n Torque. Determine the magnitudes of the force and the torque of the coil? A. F = 2 N; τ = 4 N.m B. F = 2π N; τ = 4π N.m C. F = 0 N; τ = 0 N.m D. F = 0 N; τ = 4 N.m E. F = 0 N; τ = 4π N.m 5. Sandwich 2. The diagram shows a cross-section of a straight wire carrying a flow of electrons out of the page. The wire is between the pole faces of permanent magnets. What is the direction of the magnetic force exerted on the wire? A. up B. down C. left D. right E. into the page 6. Halo. A single circular loop of radius r carries a current I. It is placed in a uniform magnetic field that is directed parallel to the plane of the loop as suggested in the figure. How will the loop rotate? A. Along the y-axis in clockwise direction as seen from the top. B. Along the y-axis in counterclockwise direction as seen from the top. C. Along the x-axis in clockwise direction as seen from the right. D. Along the x-axis in counterclockwise direction as seen from the right. E. It will not rotate. 7. Fluxes. Which of the following surfaces will have the largest magnetic flux? 2
8. Straight. An electron with velocity 7.0 m/s enters a region of uniform electric and magnetic field. If the magnitude of the E field is 21.0 N/m, what should be the magnitude of B field so that no deflection will be observed on the screen? A. 0 T B. 0.3 T C. 3.0 T D. 7.0 T E. 21.0 T 9. See. Which of the following arrows (representing direction) BEST describes the approximate direction of the magnetic force on the C-shaped current-carrying wire shown in the figure? 10. Apat-dapat 1. Four point charges are moving with equal speeds as shown by the arrows. All four charges are equidistant from point P. What the direction of the net magnetic field at point P for that particular instant of time? A. Into the page B. Out of the page C. Downward D. Upward E. No direction since the net magnetic field is zero is 11. B4 colission 1. Two positive point charges are moving towards each other with equal speeds v at an instant of time. Before the collision of the two point charges, what is the magnitude of the net magnetic field at point P with distance R and angle of 30 o from each charge? (Neglect relativistic effects.) 3
A. B. C. µ o qv 8πR 2 D. µ o qv 4πR 2 3µ o qv 4πR 2 E. zero 3µ o qv 8πR 2 12. Break na tayo! A proton and an electron move in opposite directions from the same point in space with equal speeds. If you want to measure the lowest magnitude of magnetic field produced by the two charges, where will you place the detector? All points (A to E) are equidistant from the origin. 13. Biot-Savart Law. Four wires carrying equal currents I with each having equidistant centers of wire segments dl A, dl B, dl C and dl D to point P but different thicknesses as shown in the figure. Which of the following wire segments will yield the highest magnitude of magnetic field at point P? E. All wire segments yield equal amount of magnetic field at point P 14. Field at 45 o 1. Two parallel wires carrying equal currents I in same direction as shown in the figure. What is the magnitude of magnetic field at point P due to two wire segments dl 1 and dl 2 (dl 1=dl 2=dl), each a distance r and an angle of 45 o from point P? A. B. 2µ o Idl 4πr 2 2µ o Idl 8πr 2 µ oidl C. 4πr 2 µ o Idl D. 2πr 2 E. zero 4
15. Loop. Two independent currentcarrying circular loops are lying on the plane of this paper. Loop 1 has radius r and counter-clockwise current I. Loop 2 has radius 2r and clockwise current 2I. What can be said about the (vector) magnetic fields at the axes of these loops, B 1 and B 2? A. B 1 = ½B 2 B. B 1 = -½B 2 C. B 1 = B 2 D. B 1 = -B 2 E. B 1 = -2B 2 For the next three numbers, please consider the following: Three wires carrying equal magnitudes of currents are placed parallel to each other, maintaining a distance of a between successive wires. Wires 1 and 2 are fixed at their locations, while Wire 3 is free to move. 16. Amperian loops. Which set of closed loops (that are perpendicular to the plane of this paper) should you use to evaluate the magnetic field at S? A. 3 circles, all centered at S, all with radius a. B. 3 circles, all centered at S, with radii a, 2a and 3a C. 3 circles, all centered at Wire 2, with radii a, 2a and 3a D. 3 circles: one centered at Wire 1 with radius a; one centered at Wire 2 with radius 2a; and one centered at Wire 3 with radius 3a. E. 3 circles: one centered at Wire 1 with radius 3a; one centered at Wire 2 with radius 2a; and one centered at Wire 3 with radius a. 17. Feel-ed. What is the magnetic field at point S? A. 11 µ 0I 6 2πa B. 11 µ 0I 6 2πa C. 6 µ 0I 11 2πa D. 6 µ 0I 11 2πa, out of the page, into the page, out of the page, into the page 5
E. Zero 18. Move! What will happen to Wire 3 immediately after this instant? A. It will not move. B. It will move to the left. C. It will move to the right. D. It will move out of the page. E. It will move into the page. 19. Increasing BF. A uniform magnetic field makes an angle of 60 with the central axis of a circular coil of 100 turns and a radius of 10 cm. The field changes at a rate of 20 T/s. Find the magnitude of the induced emf in the coil. A. zero B. 10π V C. 20π V D. 30π V E. 40π V 20. Insider. A circular loop enters two regions of uniform magnetic field B as shown below. What will be the direction of the induced current at the instant shown in the figure? Assume that the loop does not move very fast. A. zero B. clockwise C. counterclockwise D. out of the page E. into the page 21. Kondisyon! Consider a circular loop (fixed on the xz plane) that is immersed in a magnetic field directed along the +y-axis. Which of the following conditions will result to an induced current (I IND) in the indicated direction? I. Increasing loop area y II. decreasing loop area III. decreasing B EXT in the + y direction A. I only B. II only C. III only D. II and III only E. I, II and III I IND z x 22. Motional emf 1. A thin metallic bar of length L lying on the parallel rails of a U-shaped conductor is moving with a velocity v in a region of uniform magnetic field B directed downwards. What is the value of the induced emf produced across the bar s ends? 6 B v
A. vbl B. vbl2 C. vb/l D. v/bl E. zero 23. Induced E-field. Consider a closed loop (of radius r) in the presence of a spatially uniform but time varying magnetic field B(t) = B 0t (shown on the figure on the right). What is the magnitude of the induced electric field on the loop? A. E = B 0tπr 2 B. E = B 0πr 2 C. E = B 0r/2 D. E = B 0/2πr E. E = 0 For the next two numbers, Consider the generator set-up on the right, where a square area (initially the area vector is parallel to the magnetic field) is being rotated while immersed in a uniform B = B 0 directed downward. 24. Faraday s Law. If φ is the angle between the area vector and B, what is the induced EMF? Hint: dφ/dt = ω. A. ε = B 0Aωsin φ B. ε = - B 0Aωsin φ C. ε = B 0Aωcos φ D. ε = - B 0Aωcos φ E. ε = 0 25. Faraday s Law. At what orientations between the loop and B will the magnitude of the induced EMF be a maximum? A. When A is parallel to B (φ = 0) B. When A is anti-parallel to B (φ = 180 ) C. When A is perpendicular to B (φ = 90, 270 ) D. When A is diagonal to B (φ = 45 ) E. The induced EMF does not depend on the orientation 26. Magnetic Induction. In an induction experiment, two solenoids where used (S1 and S2). If number of turns per unit length of the solenoids are related by n 2 = 2n 1 and all other parameters are the same for both solenoids, what can be said about the magnitude of the induced EMF when identical magnets are inserted at identical speed into both solenoids? A. ε 1 > ε 2 B. ε 1 < ε 2 C. ε 1 = ε 2 D. ε 1 = ε 2 = 0 E. ε 1 > 0, ε 2 = 0 7
27. Magnetic Induction. In an induction experiment, two identical solenoids where used (S1 and S2). Identical magnets are used. The North pole of one magnet is moved towards S1, on the other hand, it is S2 that is moved toward the North pole of the other magnet. What can be said about the induced EMF if these are carried out at the same speeds? A. ε 1 > ε 2 B. ε 1 < ε 2 C. ε 1 = -ε 2 D. ε 1 = ε 2 E. ε 1 = ε 2 = 0 28. Hoops. Each of the three figures below are pairs of identical circular coils carrying identical currents, viewed from the top. Rank the three in order of increasing mutual inductance. (All figures are to scale.) i L M R A. L, M, R B. L, R, M C. M, R, L D. M, L, R E. R, M, L 29. Rel. Three series RL circuits (T, S and M) have identical resistances R, inductances L T > L S > L M, and are connected to identical batteries of emf E. Assuming zero initial current, arrange the three circuits in order of increasing time to reach 80% of the maximum current. A. T, S, M B. T, S = M C. S, T, M D. M, T, S E. M, S, T 30. Rod. Three series RL circuits (T, S and M) have identical resistances R, inductances L T > L S > L M, and are connected to identical batteries of emf E. Assuming zero initial current, arrange the three circuits in order of increasing maximum current. A. T, M, S B. M, S, T C. T, M = S D. M, S = T E. T = M = S 8
31. CLR. Three series RLC circuits (I, II and III) have the same capacitance C = 1.0 F, resistances R I = 0.5 Ω, R II = 1.0 Ω, R III = 2.0 Ω, same inductance L = 1.0 H. All capacitors are fully-charged initially. Arrange the three in order of increasing undamped frequency. A. ω I, ω II, ω III B. ω I, ω II = ω III C. ω I, ω III, ω II D. ω I = ω II, ω III E. ω I = ω II = ω III 32. Self-Inductance. An air cored solenoid of self inductance L has N turns of fine insulated copper wire with cross sectional area A. If the cross sectional area and the number of turns are doubled and the core is a medium of permeability 1000µ o, what will be the new self inductance of the coil? A. 0.004 L B. 0.008 L C. L D. 4000 L E. 8000 L 33. Toroidal Solenoid. When the current in a toroidal solenoid is changing at a rate of 0.0100 A/s, the magnitude of the induced emf is 10.0mV. When the current equals to 2.00 A, the flux through each turn of the solenoid is 0.00200 Wb. How many turns does the solenoid have? A. 10 B. 40 C. 100 D. 400 E. 1000 34. Solenoid. The magnetic energy U stored in a solenoid is 10J when the current is 2A. What should be the value of the current for the magnetic energy to be increased by a factor of 4? A. 4 A B. 8 A C. 16 A D. 32 A E. 64 A 35. L-C Circuit. Which of the following statements is TRUE regarding an L-C circuit? A. The system has a constant total energy. B. The direction of current in the circuit is the same in every cycle. C. Current oscillates with exponentially decreasing amplitude in time. D. The transformation from electric field energy to magnetic field energy varies sinusoidally. E. When the current in the inductor is maximum, the magnitude of the charge 9
in the capacitor is also maximum. 36. Elesi. A capacitor with capacitance 1.00 x 10-3 F is charged by connecting it to a 12.0 V battery. The capacitor is disconnected from the battery and connected across an inductor with inductance equal to 1.00 H. What is the initial charge of the capacitor? A. 0.0120 C B. 0.120 C C. 0 C D. 1.20 x 10 2 C E. 1.20 x 10 4 C For the next two numbers, consider a voltage source V(t) = (5 V) cos (ωt). 37. Instant V. Which phasor represents the instantaneous voltage at t = π/3ω? C B 60 60 60 60 A D E 38. RMS I. What is the rms voltage of the source? A. 0 V B. 2 V C. 5 V D. (5/ 2 )V E. 5 2 V 39. excel. What is the inductive reactance of a 10-H inductor when a current given by I = (2 A) cos [(12π rad/s)t + 3π/2] passes through it? A. 6π Ω B. 12π Ω C. 24π Ω D. 60π Ω E. 120π Ω 40. Get the Power. Consider a series RLC circuit connected to an AC voltage source (V max = 5.0V) and at resonance. If R = 1.0 Ω, C = 1.0 F and L = 1.0 H, what is the average power consumed by the circuit? A. 5.0 W B. 10.0 W 10
C. 12.5 W D. 15.0 W E. 25.0 W For the next two numbers, consider the circuit below. 41. Reso. Which of the following statements is/are true if the circuit is in resonance? I. The angular frequency of the voltage source is 0.1 rad/s II. The impedance of the circuit is 10 kω III. The current is in-phase with the voltage source A. I only B. II only C. III only D. I and II E. I, II and III 42. nans. What is the impedance of the circuit if the voltage source is dc? A. 0 kω B. 0.1 kω C. 1 kω D. 10 kω E. Infinity 43. DZUP. A student was given an inductor of inductance L=1mH. If DZUP version 2 is set at f=600hz, which of the following capacitance values used with the inductor will tune to the station s frequency? A. C= 1/(π 2 1000) F B. C= 1/(π 2 1200) F C. C= 1/(π 2 1440) F D. C= 1/(π 2 1220) F E. None of the above 11
44. Face. If you construct a hypothetical RLC circuit (R= 3 Ω, L = 4H, C = 1F) and connect it to an AC source with angular frequency 1 Hz, what is the phase angle (in radians) between your source voltage and current phasors? A. 1 B. -1 C. π D. -π E. π/4 45. ReInCa. Which of the following best describes the phasor diagram for a resistor, an inductor and a capacitor connected in series to an AC source? Toss a coin. If head, you might fail. If tail, you might also fail. END OF PROBSET 12