Physics 227 Final Wed. December 16, 2015, 4:00 PM - 7:00 PM College Ave Gym Annex (A-H), College Ave Gym (I-R) and Scott Hall 135 (S-Z)

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1 Physics 7 Final Wed. December 16, 015, 4:00 PM - 7:00 PM College Ave Gym Annex (A-H), College Ave Gym (I-R) and Scott Hall 135 (S-Z) Your name sticker with exam code 9. A proctor will check your name sticker and your student ID sometime during the exam. Please have them ready. 10. You are not allowed to help any other student, ask for help from anyone but a proctor, change your seat without permission from aproctororuseanyelectronicdevice. Doingsowillresultina zero score for the exam. 11. When you are done with the exam, hand in only this cover sheet and your answer sheet. 1. Please sign above by the name sticker to indicate that you have read and understood these instructions. SIGN HERE 1. Use a # pencil to make entries on the answer sheet. Enter the following id information now, before the exam starts.. In the section labeled NAME (Last, First, M.I.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. 3. Under STUDENT # enter your 9-digit RUID Number. 4. Under CODE enter the exam code given above. 5. Enter 7 under COURSE. You do not need to write anything else on the answer sheet for now, but you may continue to read the instructions. 6. During the exam, you are allowed three 8.5 x 11 inch sheets of paper with whatever you want written on them. NO calculators, NO cell phones. 7. The exam consists of 30 multiple-choice questions. For each question mark only ONE answer on the answer sheet. There is no deduction of points for an incorrect answer. If you cannot work out an answer, you should make an educated guess. 8. If you have questions or problems during the exam, you may raise your hand and a proctor will assist you. We will provide values of physical constants that are needed. It is your responsibility to know the relevant equations.

2 Possibly useful constants: ϵ 0 = C /N m k =1/4πϵ 0 = N m /C µ 0 =4π 10 7 T m/a = T m/a c =speedoflight= m/s q electron = q proton = C m electron =electronmass= kg m proton =protonmass= kg 1eV= J. Circumference of a circle =πr; Areaofacircleisπr Surface of a sphere = 4πr ;Volumeofasphere= 4 3 πr3 Surface area of a cylinder = πrh +πr ;Volumeofcylinder= πr h sin(0 )= cos(90 )=tan(0 )=0 sin(90 )=cos(0 )=1 sin(30 )= cos(60 )=1/ sin(60 )=cos(30 )= 3/ sin(45 )= cos(45 )= / tan(45 )= 1 tan(30 )=1/ 3 tan(60 )= 3 tanθ=sinθ/cosθ cosθ =1/ (1 + tan θ) dx n = dx nxn 1 x n = 1 n+1 xn+1 except when n = 1. For n = 1, dx/x =lnx Some metric prefixes: f=femto=10 15 p=pico=10 1 n=nano=10 9 µ =micro=10 6 m=milli=10 3 k=kilo=10 3 M=mega=10 6 G=giga=10 9

3 1. A charged capacitor stores energy U 1. Without connecting this capacitor to anything, a dielectric slab having dielectric constant K is now inserted between the plates of the capacitor, completely filling the space between them. How much energy U does the capacitor now store? a) U = U 1 /K b) U = U 1 c) U = KU 1 d) U = KU 1 e) U = U 1 /(K). A line charge with linear charge density λ extends along the x- axis from x = a to x =4a as shown in the figure. What is the potential V o at the origin? Note: k =1/4πϵ An electric dipole is formed by two charges +q and q adistanced apart as displayed in the figure. Which graph best represents the force in the y-direction F y on aprobecharge+q which is placed a distance x from the middle of the dipole along the line perpendicular to the dipole axis? a) V o = 3 kλ 4 a b) V o = 3kλa c) V o = kλ ln(4) d) V o = 3 kλ 4 a e) V o = kλ ln(4) y 0 a 4a x 3. The working element of a toaster is a nichrome wire which acts as aresistor. Allotherwireshavenegligibleresistance. Thetoaster heats up the bread by consuming 1000 W of power when plugged into a DC voltage source of 100 V. What is the resistance R of the nichrome wire? a) R = 0.10 Ω b) The information given is not sufficient we need to be given the current drawn as well. c) R = 1.0 Ω d) R = 10 Ω e) R = Ω a) Graph E b) Graph B c) Graph C d) Graph D e) Graph A

4 5. A point charge q 1 =3.0 ncislocatedonthex-axis at x =4.0 m, and a second charge q = 9.0 ncisonthey-axis at y =.0 m. What is the total electric flux Φ E due to these two point charges through a spherical surface centered at the origin and with radius r =. m? Note: ϵ C /N m. a) Φ E = N m /C b) Φ E = 10 3 N m /C c) Φ E = (/3) 10 3 N m /C d) Φ E = +(1/3) 10 3 N m /C e) Φ E = zero 6. An electromagnetic wave is traveling through vacuum. Its electric field vector is given by E = E 0 sin(kx ωt) ĵ. What is the Poynting vector S(x, t)associatedwiththisemwave? a) S(x, t) = E 0 sin (kx ωt) î b) S(x, t) = (E 0 /(µ 0 c)) sin (kx ωt) î c) d) S(x, t) = (E 0 /(µ 0 c)) cos (kx ωt) ˆk S(x, t) = E 0 sin (kx ωt) ˆk e) S(x, t) = (E 0 /(µ 0 )) cos (kx ωt) î 7. Consider an air-filled toroidal solenoid (toroid) with total number of turns N =1000,meanradiusr =1.0 mandacross-sectional area A =0.1 m.whatisthetotalinductancelof this toroidal solenoid? Note: µ 0 = 4π 10 7 T m/a. a) L = 1.0 H b) L =.0/π H c) L = 10 1 H d) L = 10 H e) L = π 10 5 H 8. In a series L R C circuit, L =.0 H,R = 00 Ω and C =µf. The voltage amplitude of the source is V 0 =100V.At the resonant angular frequency, what is the peak voltage V L,max across the inductor? a) V L,max = 100 V b) V L,max = 00 V c) V L,max = 50 V d) V L,max = 1000 V e) V L,max = 500 V 9. When two point charges are a distance d 1 apart, the electric force that each one feels from the other has magnitude F 1.Inorderto make this force twice as strong, the distance d would have to be a) d = d 1 /4 d b) d c) = d 1 / = d 1 / d) d e) d = d 1 = d For the circuit in the figure I =0.5 AandR =1Ω. Whatis the value of the EMF E? a) E = 48 V b) E = 1 V c) E = 6.0 V d) E = 18 V e) E = 4 V

5 11. A negatively charged particle is moving to the right, directly above a wire having a current flowing to the right, as shown in the figure. In which direction is the magnetic force F B exerted on the particle? a) F B is directed into the page. b) F B is directed upward. c) F B is directed out of the page. d) F B is directed downward. e) F B is zero. 1. You are given a solenoid of length Z, radiusa, andn turns per unit length with a current I 1 (t). Inside of this solenoid is one smaller loop of radius R i.e., R<A. The plane of this loop is perpendicular to the solenoid s axis. The solenoid and the loop do not touch. What is the mutual inductance M of this system? a) M = µ 0 nπr b) M = µ 0 n πr c) M = µ 0 nπa d) M = µ 0 n πr e) M = µ 0 n ZπA 14. You would like to construct an inductor that stores the same amount of energy as the energy converted to light and thermal energy by a 100-W light bulb in 1 hour. When the current in this inductor is 100-A, what is the inductance L? a) L = H b) L = H c) L = 70 H d) L = 7 H e) L = 36 H 15. As displayed in the figure, a current I flows around a rectangular loop with height w and horizontal sides b. The loop is placed in auniformmagneticfield B in such a way that the sides of length w are perpendicular to B and there is an angle θ between the sides of length b and B. What is the magnitude of the torque τ about the vertical axis of the current loop due to the interaction of the current through the loop with the magnetic field? 13. Three transformers have the following rms primary voltages V p, number of primary turns N p and number of secondary turns N s. Rank the transformers on the basis of their rms secondary voltage V s. Transformer A: V p =10V,N p =500turns,N s =000turns Transformer B: V p =40V,N p =1000turns,N s =500turns Transformer C: V p =480V,N p =000turns,N s =500turns a) V C,s > V B,s > V A,s b) V A,s > V C,s > V B,s c) V A,s > V B,s = V C,s d) V A,s = V C,s > V B,s e) V B,s > V A,s = V C,s a) τ = IbwB sin θ b) τ = IbwB c) τ = IbwB cos θ d) τ = zero e) τ = I bwb cos θ

6 16. Which of the following statements about electromagnetic (EM) waves in vacuum is FALSE? a) EM waves are transverse. b) There is a definite ratio between the magnitudes of the electric and magnetic fields of an EM wave. c) EM waves travel in vacuum with a definite and unchanging speed. d) EM waves require no medium. e) The direction of propagation of an EM wave is the same as the direction of B E. 17. Which of the following statements is TRUE? a) Inductors store energy by building up charge. b) An inductor always resists any change in the current through it. c) When an inductor and a resistor are connected in series with a DC battery, the current in the circuit reaches its maximum in one time constant. d) When it is connected in a circuit, an inductor always resists having current flow through it. e) When an inductor and a resistor are connected in series with a DC battery, the current in the circuit is zero after averylongtime. 18. A conducting bar can slide without friction across two parallel metal rails that are separated by L =.0 mandconnectedbya R =6Ωresistorasshowninthefigure. Auniformmagneticfield of B =3.0 Tisorientedperpendiculartothepage. Atwhatspeed v should the bar be moved to produce a current of I =0.5 Ain the resistor? 19. A region of space has a uniform electric field E directed towards the right, as shown in the figure. Rank the electric potentials V at points A, B, and C. a) V A = V B > V C b) V A > V B > V C c) V C > V A = V B d) V A = V B = V C e) V B > V C > V A 0. The figure displays a circular wire with radius R and uniform current density j = I/A, where I is the current in the wire and A is the cross-sectional area. What is the magnitude of the magnetic field B(r) inside the wire at a distance r < R in terms of the current I? a) B(r) = µ 0 I/(πr) b) B(r) = µ 0 I/(πR) c) B(r) = µ 0 Ir/(πR ) d) B(r) = µ 0 Ir/(πR) e) B(r) = µ 0 Ir 3 /(3R ) a) v = 6.0 m/s b) v =.0 m/s c) v = 0.5 m/s d) v = 1.0 m/s e) v = 3.0 m/s

7 1. The electric field of a sinusoidal electromagnetic wave obeys the following equation: E = (4.0 V/m)cos[(.0 10 (rad/m))x +( (rad/s))t] What is the wavelength λ of this wave? a) λ = π 10 m b) λ = π 10 m c) λ = 00 m d) λ = (π/4) m e) λ = m. A capacitor with capacitance C is charged by connecting it to a battery with voltage V.Thecapacitoristhendisconnectedfrom the battery and connected across an inductor with an inductance L. There is no resistance in this circuit. What is the maximum magnetic energy U B,max that is stored in the inductor? a) U B,max = zero. b) U B,max = V /L. c) U B,max = CV /. d) U B,max = CV /4. e) U B,max = LV /. 3. You are given a reactance of an inductor X L =100 Ω, reactance of a capacitor X C =10 Ω, and frequency = 100 Hz. Which of the following is correct? a) The inductance L = /π H b) The capacitance C = 5/π F c) The inductance L = 1H d) The capacitance C = 10 3 F e) The capacitance C = 10 3 /(π) F 4. A positive charge q moves in the x y plane with velocity v = v cos θî + v sin θĵ, i.e.,withangleθ with respect to the x axis. If the local magnetic field B is in the z direction, what are the magnitude and direction of the magnetic force F on the particle? a) F = +qvb(cos θî + sinθĵ) b) F = qvb(sin θî cos θĵ) c) F = +qvb(cos θĵ + sinθˆk) d) F = qvb(cos θî + sinθĵ) e) F = +qvb(sin θî cos θĵ) 5. The figure shows three metal coils labeled A, B, and C heading towards a region where a uniform static magnetic field B exists. The coils move with the same constant velocity v and all have the same resistance R. Their relative sizes are indicated by the background grid. When the right-hand edges of the coils have reached the dotted line, rank the induced currents I in each coil. a) I A > I B > I C b) I B = I C > I A c) I C > I B > I A d) I A = I B = I C e) I C > I B = I A

8 6. An electromagnetic wave is propagating towards the west. At a certain moment the direction of the magnetic field vector associated with this wave points vertically up. What is the direction of the electric field vector E of this wave? a) The direction of E is horizontal and points north. b) The direction of E is vertical and points up. c) The direction of E is vertical and points down. d) The direction of E is horizontal and points south. e) The direction of E is horizontal and points east. 7. You are given three circuits with the following values for capacitance C and inductance L. Circuit 1: C =1.0 µf, L =1.0 H. Circuit : C =4.0 µf, L =1.0 H. Circuit 3: C =0.5 µf, L =.0 H. Rank the resonance frequencies ω of these circuits. a) ω > ω 3 > ω 1 b) ω > ω 1 > ω 3 c) ω 3 > ω 1 = ω d) ω 1 = ω 3 > ω e) ω > ω 1 = ω 3 8. Two identical concentric loops are arranged as shown in the Figure. One loop has a steady current flowing through it (provided by a power supply). When the power is turned off, which of the following statements is TRUE? a) When the power is turned off, there is no induced current. b) When the power is turned off, the two loops will briefly attract each other and the current in loop will be clockwise. c) When the power is turned off, the two loops will briefly repel each other and the current in loop will be counterclockwise. d) When the power is turned off, the two loops will briefly attract each other. The direction of the current in loop will depend upon the intial direction of current in loop 1. e) When the power is turned off, the two loops will briefly repel each other. The direction of the current in loop will depend upon the intial direction of current in loop What resistance R should be added in series with an inductor with inductance L =6.0 HtocompleteanLR circuit with a time constant τ =3.0 ms? a) R = Ω b) R =.0 Ω c) R = Ω d) R = Ω e) R = 0.5 Ω

9 30. When an electromagnetic wave falls on a perfectly reflecting surface it exerts a force F 1 on that surface. If the surface is now replaced by a perfectly absorbing surface, what will be the force F that the same wave will exert on the surface? a) F = F 1 b) F = F 1 c) F = F 1 / d) F = 4F 1 e) F = F 1 /4

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