Final_2002Fall_Solutions

Final_2002Fall_Solutions - So I MAC Lo V’L Physics 8.02...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: So I MAC Lo V’L % Physics 8.02 Final Exam Some (possibly useful) Relations: 4? 17: -dA = 0 timed surface s d - - mils-£3} jB-dA pal}: open mar/ace closed open loop surface ~ - Ids x f- B = j dB = J' “”0 2 47: r IOUFCE (IE: 1 21—2- 4%}, r lit—1-113,; 47:60 V r Ayz’i’ikeq, i=1 "ml 10qu V=k ‘” BTHHLE r IQJ=C|AV| 2 U( _—]-C|AV|2 =9— 2 2C (1:31 E-EdVW, 2 allspace u -12 E2 1 47:5" ,uo =4Irx10'7T-m/A k = =9.0xlO°N—m2/C2 e P" H cT f=1/T co = 2791': 21t/T double slit: constructive: dsinflzml, m=0,il,i2,:3,... destructive: dsin6=[m+%]k, m:0,il!i2.i3,... single slit: TE EasinEl: ”111:, m = i1, i2, i3, Fall 2002 4 Egg 2-15% closed dt palh 8 J, It = 1—3 L () Rm} ) rzL/R r=RC a, __1_ ° JLC single slit sin[§asin9 1:1 111 EX EasinB 7L double slit I = 1m“ cos2 [9-] 2 with (1) = 2%dsin6 )2 Problem 1:(10 points) Question 1: Which of the following statement(s) correctly identifies possible sources of magnetic fields. Time chan ing electric fields .f . ‘ oPoint-like Sgtationary magnetic charges —— éOV“ t E/’( l S ‘27 a Moving point-like electric charges I. Time changing magnetic fields E. Point-like stationary electric charges I r ‘5' F. Moving point-like magnetic charges ._ 7 Cid“ T 3K L E Answer: Question 2: When a current flows in a wire of length L and cross sectional area A, the resistance of the wire is .r‘ proportional to the area A and inversely proportional to the length L aproportional to the length L and inversely proportional to the area A c) inversely proportional to the product of the length L with the area A d) proportional to the product of the length L with the area A Question 3: Suppose that at the moment shown in the figure the magnetic flux through the 100p is decreasing (in the direction indicated by the normal I": ). Is the y-component of the electric field Ey(x) . -—‘ ”‘5 _ ~J “‘4 \ @Ew‘» “it SEAR 7 O a) greater than (agrarian = [Esta-mt} Ebmflm ‘> 0 the electric field Ey (x + Ax). S Q —-— —-. EOE M J fl> Ed .90 Question 4: Suppose that at the moment shown in the figure the electric flux through the loop is increasing (in the direction indicated by the normal ii). 15 the z- componenj—l: of the __5 —-' magnetic field B (x) Q greater than %_J B 3:21,!» \iL {GL3 b) equal to c) lessthan E”? l)_z(?(+i§9()‘l' gatlw) FLAZ‘ > O the magnetic field 32 (x + Ax) ? Question 5: Coherent monochromatic plane waves impinge on two long narrow apertures that are separated by a distance (1. Each aperture has width a, with d>>a. @he adjacent interference fringes due to the double-aperture interference maxima are closer together than the distance between the adjacent diffraction minima due to the width of each aperture. b) The adjacent interference fringes due to the double-aperture interference maxima are further apart than the distance between the adjacent diffraction minima due to the width of each aperture. 0) The adjacent interference fringes due to the double—aperture interference maxima are equal to the distance between the adjacent diffraction minima due to the width of each aperture. ® Suppose that in the absence of any charges (free space), a plane sinusoidal traveling wave has an electric field of the form Problem 2: (35 points) Traveling Plane Wave and Energy E(z,t) = E“, cos[2fl (z +ct)]l. 7.— a) What direction is the wave traveling? Explain your reasoning, u n in ”Like, —'i'— JLCV‘GC‘LLO‘R, P“ CVE‘g‘K .. 50th 5i i e S acwq+ C'chegx; '3 mm 3 LC» «1. I 8 o dzicmegc z ~ C. b) Write down a vector expression for the magnetic field associated with this wave in terms of the quantities given in the electric field and any additional constants that you may need. You may find the following relationships useful éEx(2,t)=—§t—By(z,t) and %3y(z,t)=-%§7Ex(zat) a at " BCZ,"L) "—1 .. E90 COS l‘ (3+ 593 h; ”.3 ”\ . x, EXB tvi ‘- a dunes—item} as Woluived» c) What direction is the magnetic field pointing at time t = 0 on the plane 2 = 0 ? “A “ A B(Zfl> :7 -— BSD J 1 leOfi-re C“ x A . Recon/Tl WC 5 étVeClww e) Suppose this wave strikes a perfectly absorbin plane Surface of area A aligned in the x— y plane. What is the time averagea ‘radiation pressure’ that the wave exerts on the surface? '3 Problem 3: (35 points) Electric and Magnetic Fields inside a Wire and the Paynting Vector A long wire of length 5 and radius a is connected to a constant ideal voltage source AV (no internal resistance). The long wire has resistance R . (Assume the thin wire in the figure below has zero resistance). Throughout this problem, express all your answers in terms of the given quantities. a) What is the magnitude and direction of the electric field inside the wire? Assume that the current flows uniformly through the wire. E W did/c CW5!“ ES cox/YMQL/ iii—0.23% H = r“ b) Use Ampere’s Law to find the magnitude and direction of the magnetic field at a distance r S a and at a distance r 2 a from the center of the wire? Show all your work (specifically your choice of Amperian loops for each case). Answers without work will not receive any credit. Foe (‘43:, “MM \Owgliiowey éw‘éb 7' £1er :- Molten.“ c) What is the direction and magnitude of the Poynting vector S = if) x E on tho surface of the wire at r = a ? H” .7 :8 -__a r F 7777777 3"" 5 {,5 uhUJonS ‘5 .L E W7 WW: V f .4 ’ ”WM-“:1 030 HA) ’8’: V033! W? d) What is the flux of the Poynting vector, é § 12%, on the cylindrical surface of I 0 mad .mrface Kit; Q51 \uode we '3 QT'OJZ Flux @S M 2 am Ma— ,Q fig :7 M1“ H __._ 19R (Mal-Rd e) Explain how the flux of the Poynting vector on the surface of the wire is related to the time rate of change of energy inside the wire. \r eke-Straw Wail»; QWEl/ l/ 19R ‘ 5 . 3 [5 beM5 ccmrned QCCVOSS Sufi-are ‘55", ECU/f $93l2V07/CC/ at “am rate 3—9 we "EAR Problem 4: (35 points) Experiments Part 1: Microwave Experiment The transmitting antenna in the microwave experiment is shown in the figure below. A reflecting conducting plate is placed on the left and a receiving antenna is fixed in place to the right of the transmitter (not shown in figure). Approximate the radiation generated by the transmitting antenna in the microwave experiment as a plane sinusoidal wave of wavelength 7L =15cm. Assume that the amplitude of the wave is E0 = 2V] m. The speed of light c=3.0x103m/s. An ideal (zero resistance) conducting plate is a placed behind the transmitting antenna. a) What is the fre uenc of the lane wave? & 1y, 2; _ 300 arm/Sec (\ "” \, sx\0”‘m 5i ”if 7- Q X )Ooi/see: QXiO \‘iZ— b) What is the closest distance d that an ideal (zero resistance) conducting plate can be placed to the left of the transmitting antenna in order that the reflected wave from the conducting plate will interfere constructively with the transmitted wave hich is fixed in place to the right of c) What is the closest distance that an ideal (zero resistance) conducting plate can be placed to the left of the transmitting antenna in order that the reflected wave from the conducting plate will interfere destructively with the transmitted wave to produce a minimal signal at the receiver which is fixed in place to the right of the 2&2 %i Hus ides or Thomsmfi/teé . BM N+i§gibfi Lam/04% es lgo° ems: mg... W up» 1 r \ i ”fin,” D ‘ t (“.1 (AT Du: T STA/Wu eLDCSVqQEA‘Jt (1) Explain how you used the results of parts b) and c) to measure the wavelength of the radiation. \ifieuse é k$QLQVlgi ”Qt/om Max 1,0 wxlxq me we move velar: 7 Dd; Akstomc-Q A“): lac-‘54 7* ‘34) 50 (\3 ll‘mg Part II: Interference and Diffraction You are given two narrow long apertures that are separated by a distance a’ . Each aperture has width a . A plane wave of monochromatic coherent laser light of wavelength it falls on the apertures. We place the screen so that the distance D to the screen is much greater than the distance d between the apertures, D >> d . In addition, we assume that the distance between the apertures d, and the width 0 of each aperture are much greater than the wavelength of the monochromatic light, 0’ >> l , a >> 7L. a) Let y be the distance between the point P and the point 0 on the screen. If you first ignore the width of each aperture, find a relation between the distance y, the wavelength 7L, the distance between the slits d , and the distance to the screen D such that a constructive interference pattern (maximum intensity of light) will occur at the point P . BAP: Eis‘he =-W\(\ ‘ low 5mm 9) tome ewe: A; d( ['33 1‘ M/\ b) Explain qualitatively how the pattern of the intensity of the light on the screen will change if you take into consideration the effects of the width 0 of each aperture. Also explain what happens to the interference fringes if the distance between the apertures is five times the width of the aperture, 0’ = 5a. TWXTW;:\;\f Wt\\ gGCVF‘US‘e WME’W “Lt/06(— lzau LUCA/0 accouwi1wk\\ J/ See. cm Hewvtlcpeuiuvu H $2.. "in war»; (in = 8 $0pr Fa'etueg Problem 5: (35 points) Capacitance, Inductance, and the Speed of Light Consider a plane parallel capacitor of plate separation at and plate area A . The capacitor is fully charged with charge Q on the positive plate. Ignore edge effects. Throughout this problem answers without work shown will receive no credit. Express your answers in terms of the given quantities. a) Use Gauss’ 3 Law to find the direction and magnitude of the electric field b the capacitor pla es. @y show your ewe of~ Gaussian surface. 31; as _,, W450 E“ 3753 ‘ {5 '0“ b) What is the voltage difference across the plates? A V g A c) Find the capacitance C . CT- ’iiiv’: 9? A current I flows through each turn of a long air core cylindrical shaped solenoid that has N turns, length h, and radius a. C!) Use Ampere” 5 Law to find the direction and magnitude of them mgnetic field inside the solenoid. ngngrgydg: effects gm WMK e) Calculate the self-inductance L of the solenoid. The capacitor is now connected to the solenoid to form a resonant circuit without any resistance. The capacitor is initially charged with charge Q on the positive plate, and when the switch is closed the current in the circuit is found to undergo sinusoidal oscillations with period T. is i) Find an expression for the speed of light in terms of the given quantities T , N , h , a, d , and A . ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern