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# Theoretical Physics PHYSICS 721

UW

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This 11 page Class Notes was uploaded by Nichole Keebler on Thursday September 17, 2015. The Class Notes belongs to PHYSICS 721 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/205234/physics-721-university-of-wisconsin-madison in Physics 2 at University of Wisconsin - Madison.

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Date Created: 09/17/15

Lecture 2 12105 Relativsitic Electrodynamics continued 3 Spacetime diagram lightcone loss of simultaneity 4 Examples using Lorentz transformations Lorentz contraction time dilation Typical procedure a label events b apply A 5 D31 generalization simple and fancy pg 547 6 4 vectors and differential invariant length 7 7w1 w2 w3 1 11vl2 rlwlvz rlwlvg A quoty7 1 172 172 172 A 4 2 39r mlvz 1 1 1sz m mw W T T T 3 39y l zlvg 39y l z 173 1 11732 W T T 1 TT A vvAar Aar Must learn to distinguish the power from labels from context 182 alar vlmA 7 Easy method to compute proper time of an arbitrary worldline 8 Relativistic energy and momentum 115 pg 533 15 Muv2 E S Lecture 16 22305 Electrostatics 13 Conformal mapping 35104392399 WW Uz 42113 60 av 31 a W 6U Tm 39 3 Harmonic b 6U 6V 0 1 A3333 Ae T1 4 z n AzlAz2 w dgt f quot 1M 0 then 8me 0 Lecture 25 31605 Magnetostatics 5 Vector Potential and Magnetic induction for a circular current loop Jackson 55 Complete elliptic integrals 7r2 d K09 2 o 1 k3 sin 7r2 Ek d 1 k35in2 0 6 Magnetic moment 75 mow 1 3i v7L f Bl 4w l W l planar current loop 75 gjli x df I X area 7 Leading term in force and torque of a localized current distribution in an external magnetic eld energy Lecture 1 11905 Units 1 Maxwell Equations pg 557 2 Why many units 6 1 Heavisideiorentz units Appendix pg 775 SI 543 60 4 E 4 V x B 11060 1101 7 170 7XE6 zll t Gaussian 7 E247rp 4 4 13E 4 4 B77 J X 08 6 7 30 4 4 131 E770 X cfit HeavisideLorentz HL 7 Ezp 4 4 1E 14 gtltB 76i71 c t 7 30 4 4 131 E 770 X cfit 3 Going from Heavisideiorentz to SI 4 Going from Gaussian to SI Relativistic Electrodynamics 1 Goal Understand 1 S d4aTI WF W INAN 2 Introduction to special relativity 113 pg 524 Note77 17 since 0 1 Magnetostatics Lecture 28 33005 16 Examples of magnetic inductances Electrodynamics 1 Maxwell equations in medium 130 sz xia o I B A g A magnetic dipole moment spatial density 5 E 13 electiic dipole moment spatial density 2 Plane waves in a nonconducting medium Jackson 71 Lecture 6 13 105 Relativsitic Electrodynamics continued 14 Conservation 15 Action principle for EM eld Jackson 127 pg 598 1 S 145TFWF W ANJ 16 Gauge invariance preservation 8V J 0 17 Proca Equation and explicit breaking of gauge invariance Jackson 128 pg 600 18 Green s function solution to Maxwell Equations Jackson 1211 pg 612 mam WW y 7 d2f2 2m ZResimm j 1 d Resfl mw z 51mf2lzu Lecture 15 22105 Electrostatics 8 Variational approach Jackson 112 Dirichlet 1lt1gt1 g aw d3pr Neurnann 1lt1gt1 gnaw d3pr f9 dafltIgt 9 Method ofirnages Jackson 21 25 10 Green s function for sphere Jackson 26 11 Orthogonal functions expansion Jackson 28 eg periodic over A g A fE 608W Bm simw ml 2 W2 27rmz A Am gXw dxcosffx a2 V Bm Z d simwk 9 x4112 a 12 Separation of variables Jackson 29 Lecture 23 31105 Multipoles and Dielectrics 4 Electrostatic Energy in Dielectric Media W 5133 Change in energy With charges FIXED due to the introduction of a dielectric volume V With dielectric constant 52 into a dielectric With eld E1 and dielectric constant 51 AW 1 13262 CHE v El 2 V2 8W FE ng Lecture 26 31805 Magnetostatics 8 Effective current density M X Al I B A 7 x I j free current 3 1117 linear B ferromagnets 9 Mapping to electrostatics 6 l 0 V2xl 117 If f 0 and 11 is uniform 11V2ltIgtM 0 If 7 0 and W3 y 0 1 739 A 39 ltI M i ivc Ex dg lU39 47r x x 10 Examples Lecture 20 3405 Electrostatics 22 More properties of Bessel functions mm mm 1w mm mm mm b 1 a mmwwmum W l2 2 1 2 m2 2 1 2 I 2 Jmkwwdw 5a Emma 5x mm JM gm Jaw Jm1 grim Jrquot 23 Boundaryvalue problems in cylindrical coordinates Jackson 38 24 Expansion of Green Functions in Spherical Coordinates Jackson 39 victim 5lt3gt 5 i 00 l A f 7 Yln6v lylm t a1l1 1 7 Glut Z Z Wlk W 0 quot27 Lecture 21 3705 Multipoles and Dielectrics 25 Multipole expansion qzm fdgz3913nlta39 39r pltf N Z Yam Jam 7 7 2 1 7quot am Cartesian quadrupole moment Qij d335399 335 35 7quot25ij Relationship to spherical quadrupole moment eg 121 iQ23 YzmmR Z me m m Spherical tensors The value of qlm for the lowest nonvanishing multipole moment of any charge distribution is independent of the choice of origin of the coordinates

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