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Washington - PHYSICS - 119
Physics 119 Waves & Optics Lab: TAs & Sectionshttp:/courses.washington.edu/phys119/TAinfo.phpPhysics 119 Waves & Optics LabHomeMeeting Times/LocationsLab Section/T.A. InfoWebAssignFAQsCourse StructurePre-LabIn-ClassPost-LabDue DatesMake-Up
Washington - PHYSICS - 119
Physics 119 Waves & Optics Lab: WebAssignhttp:/courses.washington.edu/phys119/webassign.phpPhysics 119 Waves & Optics LabHomeMeeting Times/LocationsLab Section/T.A. InfoWebAssignFAQsCourse StructurePre-LabIn-ClassPost-LabDue DatesMake-Up Wo
Washington - PHYSICS - 119
PHYSICShttp:/www.washington.edu/students/timeschd/WIN2012/phys.html#phys119Search | Directories | Reference ToolsUW Home > Discover UW > Student Guide > Time ScheduleWinter 2012 Time ScheduleWinter Quarter 2012 Time ScheduleEnrollment and status (op
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 1 Solutions.1.5rrrA (B C)[rrrr]z = Ax (B C)y Ay (B C) x = Ax (BzC x BxCz ) Ay (ByCz BzCy )= ( A x Bz C x A x B x Cz ) ( Ay By Cz Ay Bz Cy ) + ( Az Bz Cz Az Bz Cz )rrrr= ( A x C x + Ay Cy + Az Cz ) Bz ( A
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 2 Solutions.1.32rv = xyx + 2 yzy + 3zxz2220rr v = y + 2 z + 3x2020022200 ( y + 2z + 3x )dxdydz = [ yx + 2zx + 3x / 2] dydz = [2 y + 4 z + 6]dydz= [ y + 4 zy + 6 y ] dz = [4 + 8 z + 12] dz = [4 z +
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 3 Solutions.2.2 (b replaces d )rrr221qi i1qi ( r ri ) = 4 r r 34 0 i =1 20 i =1 r rirrrrr rrr = zz r1 = (b / 2) x r2 = ( b / 2) x r r1 = r r2 = ( z 2 + b 2 / 4 )1 / 2r1 q( zz bx / 2)1 q( zz + bx /
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 4 Solutions.2.20 (assume k 0)rrr(a) E = k[ xyx + 2 yzy + 3 xzz ] E = k (0 2 y ) x + k (0 3z) y + k (0 x ) z 0 No Vrrr(b) E = k[ y 2 x + (2 xy + z 2 ) y + 2 yzz ] E = k (2 z 2 z) x + k (0 0) y + k (2 y 2 y ) z =
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 5 Solutions.2.39E 2sL = L / 0C = L /V = 2 0 L / ln(b / a)LW = 1 0 E 2 d = ( 2 / 8 2 0 ) 022b 20abs sdsddz = ( 2 / 8 2 0 ) L2 [ln( s)] aC = Q2 / 2W = 2 L2 / 2W = 2 0 L / ln(b / a)2.40P = 1 0 E 22F = PA
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 6 Solutions.3.4rrrrrrrrr E1 = / 0 E 2 = / 0 E = E1 E 2 E = 0rrrrrrrrr SVE da = (VE )d = V Ed + E Vd = ( E )2 drrrV1 = V2 on S V = V1 V2 = 0 on S (E) 2 dt = SVE da = 0V1 /n = V2 /n on S V /n = 0 on S
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 7 Solutions.3.7(b)V ( r, ) =Er =q1q122 1/ 2 24 0 [ r 2 ra cos + a ]4 0 [( ra / R) 2 ra cos + R 2 ]1 / 2q( r a cos )q( ra 2 / R 2 a cos )4 0 [ r 2 2 ra cos + a 2 ]3 / 2 4 0 [( ra / R) 2 2 ra cos + R 2
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 8 Solutions.3.1631 d 21 d3 63423P3 ( x ) = 3 ( x 1) =3 ( x 3 x + 3 x 1) = (5 x 3 x ) / 22 3! dx 48 dx(1 x 2 ) d 2 P3 ( x ) / dx 2 2 xdP3 ( x ) / dx + 3( 3 + 1) P3 ( x )= (1 x 2 )15 x 2 x (15 x 2 3) / 2 +
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 9 Solutions.3.27Q = 3q 2q 2q + q = 0P = 3q( az ) + ( 2q)( ay ) + ( 2q)( ay ) + q( az ) = 2qazQp r2qaz rqa cosV=++2 + = 0 +2 + =4 0 r 4 0 r4 0 r2 0 r 23.29V ( r ) = q / 4 0 r z / 2 q / 4 0 r + z / 22
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 10 Solutions.4.9q at origin,p at r ,p r = pr cos F = ( p ) EE = qr / 4 0 r 3 qxpx q3 px qx 2 3 py qxy 3 pzqxzFx = px + py + pz =yz 4 0 ( x 2 + y 2 + z 2 ) 3 / 2 4 0 r 3 4 0 r 5 4 0 r 5 4 0 r 5 x = [
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 11 Solutions.5.1( R s) 2 + a 2 = R 2F = qvB = mv 2 / RR 2 2 Rs + s2 + a 2 = R 2R = (s2 + a 2 ) / 2smv = qBR = qB( s2 + a 2 ) / 2 s B = ( kz) /x = 0 OKa /22Bottom F1 = I a / 2 ydy k ( a / 2) x = 1 Ika 2 za /
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 12 Solutions.5.13 B d = 0Ienc(a) s < aB = B( s)=0B =0Ienc Jda = (b) J = kss<aIenc =s>aI=as>aIenc = IB2s = 0 Iks2sds = 2ka 3 / 3B = 0 I / 2sk = 3I / 2a 3same as (a)0sks+2s+ds+ = 2ks3 / 3 = Is
Georgia Tech - PHYS - 3122
Physics 3122, Fall 2010: Homework Set 13 Solutions (not graded).6.1 ( x horizontal and y vertical)m1 = Ia 2 y m2 = Ib 2 xr = rxB = 0 [ 3( m1 r ) r m] / 4 r 3 = 0 [0 Ia 2 y ] / 4 r 3 = 0 Ia 2 y / 4 r 3N = m2 B = ( Ib 2 x ) ( 0 Ia 2 y / 4 r 3 ) = 0 I 2
Georgia Tech - PHYS - 3122
Average Electric Field due to Charges in a Sphere Ian R. Gatland, Georgia Institute of Technology Phys 3122 Notes, June 22, 2010 Consider a charge q on the zaxis at a distance z above the origin inside a sphere
Georgia Tech - PHYS - 3122
Legendre Generating Function.Ian R. Gatland, Georgia Institute of Technology.Physics 3122 Notes, June 17, 2010.The electrostatic potential isV (r ) =14 0 ( r+) d +| r r+ |(1)and| r r+ |1 = [ r 2 2 rr+ cos + r+2 ]1 / 2= r1[1 2( r+ / r) c
Georgia Tech - PHYS - 3122
Legendre Polynomials Rodrigues Formula.Ian R. Gatland, Georgia Institute of Technology.Physics 3122 Notes, June 17, 2010.The differential equation for the Legendre polynomials, P ( x ) , is(1 x 2 ) P++( x ) 2 xP+( x ) + ( + 1) P ( x ) = 0and a sol
Georgia Tech - PHYS - 3122
Line Integral. Ian R. Gatland, Georgia Institute of Technology Physics 3122 notes, September 2, 2010 Consider a line integral, v d , where the points on the line are specified in terms of some parameter, t, as x
Georgia Tech - PHYS - 3122
Magnetic Moment. Ian R. Gatland, Georgia Institute of Technology Physics 3122 Notes, July 22, 2010 Preliminaries. Consider a vector field, J ( r ) , that is localized (zero on and outside a surface S surrounding a
Georgia Tech - PHYS - 3123
Physics3123Homework8(due3/18/11)Griffithschapter9:9.19(6points)1) TransmissionthroughametalfoilAplaneE&Mwave(frequency)isincidentnormallyonaconductingfoilofconductivity(dielectricconstant,magneticpermeability)andthicknessd.Thefoilisthickenoughthatmu
Georgia Tech - PHYS - 3123
Physics3123Homework9(due4/1/11)Griffithschapter9:9.29(6points)HollowwaveguidesShowthattheTEwavesthatwefoundinclasssatisfytheboundaryconditionsimposedbyaperfectlyconductingshell(wecheckedsome,butnotallconditionsinclass).(6points)Griffithschapter10:
Georgia Tech - PHYS - 3123
Physics3123Homework10(due4/8/11)1)PleasederivetheLienardWiechertformulaforthevectorpotentialofamovingpointchargestartingfromtheretardedpotentials,Eq.10.19ofGriffiths.(9points)2)Considerapointchargeqthatismovingonacircularorbitofradiusbwithconstantangu
Georgia Tech - PHYS - 3123
Physics3123Homework11(due4/22/11)1)PleasecomputethetimederivativeoftheLinardWiechertvectorpotentialofamovingpointcharge.(9points)2)Considertheradiationcontributiontothemagneticfieldofapointchargeq,whichmovesnonrelativistically(v<c)onalocalizedorbitw(t
Georgia Tech - PHYS - 3123
Physics 3123 (Spring 2011), 1st Quiz3/4/111. A straight wire that coincides with the x-axis of a cartesian coordinatesystem carries current I. A conducting, rectangular loop with sides a (|x)and b (|y ) moves with velocity v = v y away from the wire.
Georgia Tech - PHYS - 3123
Q *it I-6p(*1,0,^5.Tt,3# =-tr.([t_?,r t-iT.Tprl-+tt1t: o lttJ- aE.\ri, \ - b.(*r?I1 .rotr=-Y'\aEcfw_it= ( [* v Lh /^F\Jtt1T:q:nl(lop\(Lnllrv^d4.tSk * v t$-=.rdr -*R\1u_utr T'rv o.p"I/tr 1 ;fu-'tl- -\tt
Georgia Tech - PHYS - 3123
Physics 3123 (Spring 2011), 2nd Quiz4/8/111. Calculate the reection coecient for light at an air-to-copper interface(air copper 0 , air 0 , copper = 6.0 107 1 m1 ) at opticalfrequencies ( = 4 1015 /s). Use that copper copper . The numericalresult is
Georgia Tech - PHYS - 3123
Georgia Tech - PHYS - 3123
Physics3123,Electro&Magnetostatics,Spring2011Instructor: Markus Kindermann, Rm. C203Email:markus.kindermann@physics.gatech.eduOffice hours: by appointmentClass TAs:Adam Kamor, Rm W503, akamor@gmail.comLaminack, William, wlaminack3@gatech.eduOffice
Georgia Tech - PHYS - 3141
PHYS 3141 Midterm ExamSpring 2010Problem 1: The box on the left has adiabatic walls. A partition separatesa region lled with gas from a region of vacuum. At a certain moment, thepartition disintegrates and the gas expands to ll the entire box. The nal
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Assignment 1, Fall 2010: due 9/7 inclassNotation: We use t to denote /t, etc.1. (a) The (angular) frequency, > 0, and wavenumber, k , of light propagating in thevacuum are related by = c|k |, where c is the speed of
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Assignment 8, Fall 20101. (a) The spin-1/2 operators act on a vector space C2 of state vectors. Find the normalizedeigenvectors and eigenvalues of the Pauli matrices,100 i01. and z = , y = x = 0 1i010Clearl
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Assignment 2, Fall 20101. To justify the energy eigenfunction expansion for the wave function of a particle in abox x [0, a] it is useful to know that any square integrable function dened on the rangex [a, a] can be w
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Assignment 3, Fall 20101. Griths problem 2.7 p. 39 ( Read examples 2.2 and 2.3 before you answer.)2. Consider the Fourier transform of the wave function (x, t),(p, t) =dx ipx/e(x, t),2and the inverse Fourier tran
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Assignment 4, Fall 201021. (a) Substitute (x, t) = Aex eit/2 into the time dependent Schrodinger equation fora particle of mass m, and determine for which potential V (x) and which value of it is astationary state.(
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Assignment 5, Fall 20101. (a) Show that the wave function,nit/2z (x, t) = N en=0(zeit )un (x),n!with z a complex number, satises the time-dependent Schrodinger equation i = H ,tfor the harmonic oscillator whos
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Assignment 6, Fall 20101. Consider scattering from a step potential 0, x < 0;V (x) = V0 , x 0.Suppose that incoming particles from x = , with energy E , are incident on the interface.Calculate the incident, reected
Georgia Tech - PHYS - 3143
1APPENDIX 1: COMPLEX NUMBERS AND PROBABILITYA.Complex numbers and wave interferenceThe number i satises i2 = 1. Let us write a general complex number in cartesian and polar forms as z = x + iy =rei , where x = Re(z ) and y = Im(z ) are real numbers,
Georgia Tech - PHYS - 3143
1APPENDIX 2: BOUND STATES IN ONE DIMENSIONAL PROBLEMSA.Bound state energy levels are non-degenerate in one dimension.Let us consider the hypothesis that there are two linearly independent eigenfunctions u1 and u2 corresponding tothe same energy eigen
Georgia Tech - PHYS - 3143
1ADDITIONAL COMMENTS ON HERMITIAN OPERATORSThe remarks below are not intended to be complete. Rather, they supplement the material given in the lecture ofOctober 5, 2010.The theory of Hermitian[1] operators arises naturally in quantum theory. In the l
Georgia Tech - PHYS - 3143
1BACKGROUND QUANTUM PHYSICS 1900-1925In these notes we briey discuss several of the important developments in quantum physics in the period 1900-1925before the invention of quantum mechanics by Heisenberg and Schrodinger [1, 2]. Blackbody radiation (P
Georgia Tech - PHYS - 3143
1PHYS 3143 QUANTUM MECHANICS I: REMARKS ON THE VECTOR SPACE FORMALISMBrian Kennedy, School of Physics, Georgia TechThe notes below are not intended to be complete, but I hope you will nd them useful. They are supposed tosupplement the class notes and
Georgia Tech - PHYS - 3143
1PROBABILTY AMPLITUDES AND WHICH PATH INFORMATIONThe following, rather qualitative discussion is adapted from Feynmans lectures on physics Vol III, Chapter 3. Itserves to give us a avor of quantum mechanics and to motivate pictorially some of the theor
Georgia Tech - PHYS - 3143
Georgia Tech - PHYS - 3143
Quantum Mechanics I, Physics 3143: Quiz 2, Fall 20091. (a) What is the inner product | on the complex vector space CN of N 1 column1 2matrices, | ? . N(b) A hermitian operator A satises A| = |A . Which of the following operatorsare hermitian ?
Georgia Tech - PHYS - 3201
PHYS 3201 TEST 2April 14, 20101.) Disk in a Bowl00.10.20.3R0.40.50.60.70.8r0.9110.80.60.40.200.20.40.60.81A disk of mass M , moment of inertia I , and radius r is placed in a bowl of radius R, where R r.Assume the disk rolls wi
Georgia Tech - PHYS - 3201
1.11) Waves On a StringString has mass m, length l and tension . The speed of wave has dimensions[v ] =LTwhile the quantitites listed above have dimensions[m] = M[l] = L[ ] = M L/T 2So to match dimensions[m l ] = [v ]we must have++2LMT=
Georgia Tech - PHYS - 3201
3.29) Atwoods Three@@'$'$&%&%'$umu3m&%u2m6x+Dene the positions of the three masses as x1 , x2 , and x3 , with the positive xdirection dened as up in the gure. Summing the forces on each mass revealsmx12mx23mx3===2mg2mg3mgwith the
Georgia Tech - PHYS - 3201
4.17) Eective Spring ConstantFirst consider two springs with constants k1 , k2 in parallel. When they arestretched from their equilibirum length by a distance x, the force isFx = k1 x k2 x = ke xso we seeke = k1 + k2Now consider two springs in serie
Georgia Tech - PHYS - 3201
5.32) Cart in a ValleyThe carts initial potential energy is mgh1 There is no initial kinetic energy(cart is said to be at rest), so this is the total energy of the cart. As a quantitym of sand leaks out of the cart, the carts energy will be reduced by
Georgia Tech - PHYS - 3201
5.68) Maximum P and E of a RocketThe rocket begins at rest with mass M , ejecting exhaust at speed u. We can useequation 5.54 to nd the rockets current speed as a function of its remainingmass m(t)Mv (t) = u logm(t)the rockets forward momentum is m
Georgia Tech - PHYS - 3201
6.25) Spring on a TWe can express the masses position in cartesian coordinates asxy= l cos = l sin +r sin r cos where r is the displacement of the mass along the cross-bar, and is the angle thearm from the origin to the cross-bar (with lenght l)
Georgia Tech - PHYS - 3201
Triangular Pendulumdene as the pendulums angle of rotation. We can nd the kinetic energy of the pendulum from itsvelocity. Since both masses are moving in polar coordinates at constant radius l, their velocity is simply land1T = m(l2 2 + l2 2 ) = ml2
Georgia Tech - PHYS - 3201
7.13) Intersecting OrbitsThe two masses will orbit about their common center of mass, with the mass m always twice as far from thecenter of mass as the mass 2m.The minimal eccentricity for the two orbits to intersect will have the closestapproach for t
Georgia Tech - PHYS - 3201
8.58) Pendulum CollisonThe energy of the stick can be expressed as a sum of the energy of the eective point mass atthe stick center of mass, and the sticks rotational kinteic energy about that point. The rotationalenergy is11Trot = I 2 = ml2 2224
Georgia Tech - PHYS - 3202
Legendre TransformationShina TanLegendre transformation is useful in both mechanics and thermodynamics.Given any smooth function f (x) dened in the domain x1 < x < x2 , if f (x) > 0 for allx in this domain, so that f (x) is strictly convex1 , we can d
Georgia Tech - PHYS - 3202
Variational methods in which TIME is also variedShina TanWe traditionally x the time variable of a path in the variations.In relativity, however, time is intimately related to space. Time and space are mixedif we go from one reference frame to a diere
Georgia Tech - PHYS - 3202
PHYS 3202 Classical Mechanics II - Homework #1Due at 12:05pm, Friday Jan 28, 2011 in the classIn all homework solutions, quizzes, and nal exam, please show intermediate steps of your calculations. Whenever appropriate, you may drawdiagram(s) in your so
Georgia Tech - PHYS - 3202
PHYS 3202 Classical Mechanics II - Homework #2Due at 12:05pm, Friday Feb 4, 2011 in the classIn homework, quizzes, and nal exam, please show intermediate stepsof your calculations. Whenever appropriate, you may draw diagram(s).Problem 1 (10 points): T
Georgia Tech - PHYS - 3202
PHYS 3202 Classical Mechanics II - Homework #3Additional HintsProblem 1. Part 1- The circle isr = constant,z = another constantin the cylindrical coordinate system.See Appendix F.2 of Thornton and Marion, 5th Edition for information about thecylind