{"id":420,"date":"2023-09-05T22:18:38","date_gmt":"2023-09-05T22:18:38","guid":{"rendered":"https:\/\/physics.uri.edu\/muller\/?page_id=420"},"modified":"2023-09-06T14:33:49","modified_gmt":"2023-09-06T14:33:49","slug":"phy331n","status":"publish","type":"page","link":"https:\/\/physics.uri.edu\/muller\/phy331n\/","title":{"rendered":"PHY331N"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">Teaching<\/h1>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"sub_nav\"><a title=\"Electricity and Magnetism\" href=\"https:\/\/physics.uri.edu\/muller\/phy331n\/\">PHY331<\/a>|<a title=\"Mathematical Methods of Physics I\" href=\"https:\/\/physics.uri.edu\/muller\/phy510n\/\">PHY510<\/a> |<a title=\"Equilibrium Statistical Physics\" href=\"https:\/\/physics.uri.edu\/muller\/phy525n\/\">PHY525<\/a><\/div>\n\n\n\n<div>&nbsp;<\/div>\n\n\n\n<p><a rel=\"license\" href=\"http:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\"><img decoding=\"async\" style=\"border-width: 0;\" src=\"https:\/\/i.creativecommons.org\/l\/by-nc-sa\/4.0\/88x31.png\" alt=\"Creative Commons License\"><\/a>This work is licensed under a <a rel=\"license\" href=\"http:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License<\/a>.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Electricity and Magnetism<\/h1>\n\n\n\n<p>This topic outline is incomplete in many respects. Updates are being posted periodically.<\/p>\n\n\n\n<p>These lecture notes are for&nbsp;the advanced undergraduate course PHY331 and for the graduate courses PHY530\/PHY630.<\/p>\n\n\n\n<p>In PHY331 the goal is cover parts of the first 14 modules and some of the simpler exercises.<\/p>\n\n\n\n<p>In PHY530 parts of most earlier modules serve as review materials. The goal is to cover the first 14 modules in more depth and focus on the more advanced applications\/exercises.<\/p>\n\n\n\n<p>In PHY630 students are expected to be familiar with the materials of at least the first 11 modules. Nevertheless, some key concepts from the early modules will be briefly reviewed.&nbsp;The later modules are more topical in nature and need not be covered in any particular sequence.<\/p>\n\n\n\n<p>Depending on the level of preparedness of the students in class, adjustments will be made in each course.<\/p>\n\n\n\n<p>A different set of lecture notes and slides for a one-semester introductory course on electricity and magnetism (PHY204) is available elsewhere:<br><a href=\"http:\/\/www.phys.uri.edu\/gerhard\/PHY204\/lecslif14.html\">http:\/\/www.phys.uri.edu\/gerhard\/PHY204\/lecslif14.html<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Electrostatics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln5.pdf\">[lln5]<\/a>&nbsp;<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coulomb force between point charges<\/li>\n\n\n\n<li>Coulomb force mediated by electric field<\/li>\n\n\n\n<li>Charge densities<\/li>\n\n\n\n<li>Electric potential<\/li>\n\n\n\n<li>Gauss&#8217;s law for the electric field<\/li>\n\n\n\n<li>Electric flux<\/li>\n\n\n\n<li>Electrostatic field at surfaces and interfaces<\/li>\n\n\n\n<li>Electrostatic field determined via Gauss&#8217;s law<\/li>\n\n\n\n<li>Electrostatic energy<\/li>\n\n\n\n<li>Differential relations versus integral relations<\/li>\n\n\n\n<li>Electrostatic force on extended charged object<\/li>\n\n\n\n<li>Interaction energy and self-energy for extended charged objects<\/li>\n\n\n\n<li>Multipole expansion<\/li>\n\n\n\n<li>Torque and force on electric dipole<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Electric field of a charged rod I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex1.pdf\">[lex1]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric field of a charged ring I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex2.pdf\">[lex2]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric field of a charged spherical shell&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex3.pdf\">[lex3]<\/a>&nbsp;&nbsp;<\/li>\n\n\n\n<li>Electric field of a charged ring II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex4.pdf\">[lex4]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric field of a charged rod II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex5.pdf\">[lex5]<\/a>&nbsp;&nbsp;<\/li>\n\n\n\n<li>Electric field of a charged rod III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex6.pdf\">[lex6]<\/a>&nbsp;&nbsp;<\/li>\n\n\n\n<li>Electric field of V-shaped line charge&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex7.pdf\">[lex7]<\/a>&nbsp;&nbsp;<\/li>\n\n\n\n<li>Electric field of parabolic line charge&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex8.pdf\">[lex8]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric dipole field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex9.pdf\">[lex9]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electrostatic field of two point charges&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex39.pdf\">[lex39]<\/a><\/li>\n\n\n\n<li>From electric potential to electric field and back&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex40.pdf\">[lex40]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric flux through cube and net charge inside&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex41.pdf\">[lex41]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric potential of charged rod&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex42.pdf\">[lex42]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric field of uniformly charged concentric spheres&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex46.pdf\">[lex46]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric field of uniformly charged coaxial cylinders&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex47.pdf\">[lex47]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electrostatic interaction energy of point charges&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex120.pdf\">[lex120]<\/a><\/li>\n\n\n\n<li>Electric field generated by linear arrays of point charges&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex128.pdf\">[lex128]<\/a><\/li>\n\n\n\n<li>Electrostatic force between two point charges&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex187.pdf\">[lex187]<\/a><\/li>\n\n\n\n<li>Oppositely charged semicircles&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex188.pdf\">[lex188]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric field of planar charge distributions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex189.pdf\">[lex189]<\/a><\/li>\n\n\n\n<li>Electric potential of charged ring I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex192.pdf\">[lex192]<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Self-energy and interaction energy of point charges&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam8.pdf\">[lam8]<\/a><\/li>\n\n\n\n<li>Surface electric dipole layers&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam9.pdf\">[lam9]<\/a><\/li>\n\n\n\n<li>Green&#8217;s theorem&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam11.pdf\">[lam11]<\/a>&nbsp;<\/li>\n\n\n\n<li>Mathematica syntax items for E&amp;M&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam21.nb\">[lam21.nb]<\/a><\/li>\n\n\n\n<li>Vector analysis&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/gmd1.pdf\">[gmd1]<\/a>&nbsp;<\/li>\n\n\n\n<li>Generalized functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/gmd3.pdf\">[gmd3]<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. Electrostatics II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln6.pdf\">[lln6]<\/a>&nbsp;<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Electrical insulators and conductors<\/li>\n\n\n\n<li>Electrostatic properties of conductors<\/li>\n\n\n\n<li>Specifications of conductors at equilibrium<\/li>\n\n\n\n<li>Electric field at the surface of a conductor<\/li>\n\n\n\n<li>Electrostatic pressure<\/li>\n\n\n\n<li>Existence and uniqueness of electrostatic equilibrium<\/li>\n\n\n\n<li>Boundary value problem<\/li>\n\n\n\n<li>Electric field in empty cavity<\/li>\n\n\n\n<li>Capacitor<\/li>\n\n\n\n<li>Method of images for induced charges<\/li>\n\n\n\n<li>Solutions in search of a problem<\/li>\n\n\n\n<li>Applications with planar, spherical, or cylindrical symmetry<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Parallel-plate capacitor&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex10.pdf\">[lex10]<\/a><\/li>\n\n\n\n<li>Cylindrical capacitor&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex11.pdf\">[lex11]<\/a><\/li>\n\n\n\n<li>Spherical capacitor&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex12.pdf\">[lex12]<\/a><\/li>\n\n\n\n<li>Point charge near plane conducting surface&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex13.pdf\">[lex13]<\/a><\/li>\n\n\n\n<li>Electric dipole near plane conducting surface I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex14.pdf\">[lex14]<\/a><\/li>\n\n\n\n<li>Electric dipole near plane conducting surface II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex15.pdf\">[lex15]<\/a><\/li>\n\n\n\n<li>Point charge near perpendicular plane conducting surfaces&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex16.pdf\">[lex16]<\/a>&nbsp;<\/li>\n\n\n\n<li>Conducting sphere in uniform electric field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex17.pdf\">[lex17]<\/a><\/li>\n\n\n\n<li>Line charge near plane conducting surface&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex18.pdf\">[lex18]<\/a><\/li>\n\n\n\n<li>Conducting cylinder in uniform electric field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex19.pdf\">[lex19]<\/a>&nbsp;<\/li>\n\n\n\n<li>Conducting hyperbolic trough&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex43.pdf\">[lex43]<\/a><\/li>\n\n\n\n<li>Conducting sphere between point charges&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex124.pdf\">[lex124]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Electric potential of point charge near conducting sphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam10.pdf\">[lam10]<\/a><\/li>\n\n\n\n<li>Coordinate systems&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/gmd2.pdf\">[gmd2]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. Electrostatics III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln7.pdf\">[lln7]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Uniqueness theorem for Laplace equation<\/li>\n\n\n\n<li>Separable solutions in Cartesian coordinates<\/li>\n\n\n\n<li>Separable solutions in spherical coordinates<\/li>\n\n\n\n<li>Separable solutions in cylindrical coordinates<\/li>\n\n\n\n<li>Solutions from conjugate functions<\/li>\n\n\n\n<li>Application to charged plane surface<\/li>\n\n\n\n<li>Application to charged cylindrical surface<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Square pipe made of conducting walls at different potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex20.pdf\">[lex20]<\/a><\/li>\n\n\n\n<li>Conducting rectangular pipe with end-plate potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex21.pdf\">[lex21]<\/a><\/li>\n\n\n\n<li>Conducting hemispherical shells at different electric potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex22.pdf\">[lex22]<\/a><\/li>\n\n\n\n<li>Oppositely charged hemispherical shells&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex23.pdf\">[lex23]<\/a><\/li>\n\n\n\n<li>Series expansion of off-center Coulomb potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex24.pdf\">[lex24]<\/a><\/li>\n\n\n\n<li>Conducting half-cylindrical shells at different electric potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex25.pdf\">[lex25]<\/a><\/li>\n\n\n\n<li>Conducting plates intersecting at right angle&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex26.pdf\">[lex26]<\/a><\/li>\n\n\n\n<li>Electric potential and field at edge of large conducting plate&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex27.pdf\">[lex27]<\/a><\/li>\n\n\n\n<li>Fringe electric potential and field of parallel plates&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex28.pdf\">[lex28]<\/a><\/li>\n\n\n\n<li>Conducting hemispheres at opposite electric potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex125.pdf\">[lex125]<\/a><\/li>\n\n\n\n<li>Electrostatic potential inside rectangular box I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex126.pdf\">[lex126]<\/a><\/li>\n\n\n\n<li>Electrostatic potential inside rectangular box II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex127.pdf\">[lex127]<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Meaning of Orthogonality&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam15.pdf\">[lam15]<\/a>&nbsp;<\/li>\n\n\n\n<li>Expansions in orthogonal functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam12.pdf\">[lam12]<\/a><\/li>\n\n\n\n<li>Laplace equation in spherical coordinates&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam13.pdf\">[lam13]<\/a>&nbsp;<\/li>\n\n\n\n<li>Laplace equation in cylindrical coordinates&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam14.pdf\">[lam14]<\/a>&nbsp;<\/li>\n\n\n\n<li>Legendre polynomials and functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam16.pdf\">[lam16]<\/a><\/li>\n\n\n\n<li>Spherical Harmonics&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam17.pdf\">[lam17]<\/a><\/li>\n\n\n\n<li>Bessel functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam18.pdf\">[lam18]<\/a><\/li>\n\n\n\n<li>Multipole expansion generalized&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam19.pdf\">[lam19]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4. Dielectrics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln9.pdf\">[lln9]<\/a>&nbsp;<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Induced electric dipole moments<\/li>\n\n\n\n<li>Polar molecules<\/li>\n\n\n\n<li>Polarization and bound charge<\/li>\n\n\n\n<li>Displacement field<\/li>\n\n\n\n<li>Boundary conditions involving dielectrics<\/li>\n\n\n\n<li>Linear dielectrics<\/li>\n\n\n\n<li>Poisson equation for uniform linear dielectric<\/li>\n\n\n\n<li>Clausius-Mossotti model<\/li>\n\n\n\n<li>Energy density in dielectric<\/li>\n\n\n\n<li>Capacitance with dielectric<\/li>\n\n\n\n<li>Impact of dielectric added to capacitor<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Uniformly polarized dielectric sphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex29.pdf\">[lex29]<\/a>&nbsp;<\/li>\n\n\n\n<li>Dielectric sphere polarized by uniform electric field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex30.pdf\">[lex30]<\/a><\/li>\n\n\n\n<li>Lateral force on dielectric slab between parallel plates&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex31.pdf\">[lex31]<\/a>&nbsp;<\/li>\n\n\n\n<li>Point charge near plane surface of dielectric I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex32.pdf\">[lex32]<\/a>&nbsp;<\/li>\n\n\n\n<li>Capacitor with stacked dielectrics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex44.pdf\">[lex44]<\/a>&nbsp;<\/li>\n\n\n\n<li>Capacitor with stacked dielectrics II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex45.pdf\">[lex45]<\/a><\/li>\n\n\n\n<li>Point charge near plane surface of dielectric II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex48.pdf\">[lex48]<\/a>&nbsp;<\/li>\n\n\n\n<li>Insertion of conducting slab between capacitor plates I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex53.pdf\">[lex53]<\/a><\/li>\n\n\n\n<li>Insertion of conducting slab between capacitor plates II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex54.pdf\">[lex54]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mesoscopic fields and sources&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam20.pdf\">[lam20]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">5. Electric Currents I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln11.pdf\">[lln11]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Electric current density<\/li>\n\n\n\n<li>Electric current<\/li>\n\n\n\n<li>Charge conservation<\/li>\n\n\n\n<li>Ohm&#8217;s law<\/li>\n\n\n\n<li>Device with capacitance and resistance<\/li>\n\n\n\n<li>Electric field driving steady current<\/li>\n\n\n\n<li>Classical model of conductivity<\/li>\n\n\n\n<li>Power dissipation in resistive materials<\/li>\n\n\n\n<li>Electric current in vacuum tube<\/li>\n\n\n\n<li>Resistor circuits in steady state<\/li>\n\n\n\n<li>Capacitor circuits at equilibrium<\/li>\n\n\n\n<li>RC circuits<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Charge accumulated in conductor with steady current&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex33.pdf\">[lex33]<\/a><\/li>\n\n\n\n<li>Capacitor circuit I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex34.pdf\">[lex34]<\/a>&nbsp;<\/li>\n\n\n\n<li>Resistor circuit I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex35.pdf\">[lex35]<\/a><\/li>\n\n\n\n<li>Resistor circuit II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex49.pdf\">[lex49]<\/a>&nbsp;<\/li>\n\n\n\n<li>Capacitor circuit II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex55.pdf\">[lex55]<\/a>&nbsp;<\/li>\n\n\n\n<li>Capacitor circuit III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex56.pdf\">[lex56]<\/a><\/li>\n\n\n\n<li>RC circuit I at equilibrium&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex57.pdf\">[lex57]<\/a><\/li>\n\n\n\n<li>RC circuit I with currents flowing&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex58.pdf\">[lex58]<\/a>&nbsp;<\/li>\n\n\n\n<li>RC circuit I: transfer of energy between devices&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex61.pdf\">[lex61]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">6. Magnetostatics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln12.pdf\">[lln12]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Lorentz force<\/li>\n\n\n\n<li>Magnetic force on a charged particle<\/li>\n\n\n\n<li>Magnetic force on current-carrying conductor<\/li>\n\n\n\n<li>Biot-Savart law<\/li>\n\n\n\n<li>Magnetic flux<\/li>\n\n\n\n<li>Gauss&#8217;s law for the magnetic field<\/li>\n\n\n\n<li>Amp\u00e8re&#8217;s law restricted to steady states<\/li>\n\n\n\n<li>Steady-state magnetism and electrostatics<\/li>\n\n\n\n<li>Consistency of the Biot-Savart law with Amp\u00e8re&#8217;s law<\/li>\n\n\n\n<li>Vector potential<\/li>\n\n\n\n<li>Magnetic dipole moment<\/li>\n\n\n\n<li>Torque and force on magnetic dipole<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Magnetic dipole field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex36.pdf\">[lex36]<\/a><\/li>\n\n\n\n<li>Motion in crossed electric and magnetic fields&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex50.pdf\">[lex50]<\/a><\/li>\n\n\n\n<li>Magnetic field of straight current segment I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex51.pdf\">[lex51]<\/a><\/li>\n\n\n\n<li>Magnetic field of straight current segment II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex52.pdf\">[lex52]<\/a><\/li>\n\n\n\n<li>Magnetic field of a circular current I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex59.pdf\">[lex59]<\/a><\/li>\n\n\n\n<li>Magnetic field of a square-shaped wire&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex60.pdf\">[lex60]<\/a><\/li>\n\n\n\n<li>Velocity selector&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex62.pdf\">[lex62]<\/a><\/li>\n\n\n\n<li>Magnetic moment of rotating charged disk&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex63.pdf\">[lex63]<\/a><\/li>\n\n\n\n<li>Magnetic moment of rotating charged spherical shell&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex64.pdf\">[lex64]<\/a><\/li>\n\n\n\n<li>Magnetic field along the axis of a solenoid&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex65.pdf\">[lex65]<\/a>&nbsp;<\/li>\n\n\n\n<li>Mass spectrometer&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex71.pdf\">[lex71]<\/a><\/li>\n\n\n\n<li>Magnetic moment of rotating charged solid sphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex78.pdf\">[lex78]<\/a>&nbsp;<\/li>\n\n\n\n<li>Helmholtz coil and beyond&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex129.pdf\">[lex129]<\/a>&nbsp;<\/li>\n\n\n\n<li>Magnetic dipole interaction I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex130.pdf\">[lex130]<\/a><\/li>\n\n\n\n<li>Magnetic dipole interaction II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex131.pdf\">[lex131]<\/a><\/li>\n\n\n\n<li>Magnetic dipole interaction III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex133.pdf\">[lex133]<\/a><\/li>\n\n\n\n<li>Magnetic dipole interaction IV&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex148.pdf\">[lex148]<\/a><\/li>\n\n\n\n<li>Current density and magnetic dipole moment&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex190.pdf\">[lex190]<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Principle of relativity&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam27.pdf\">[lam27]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">7. Magnetostatics II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln13.pdf\">[lln13]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Magnetic dipole moments of elementary particles<\/li>\n\n\n\n<li>Electric and magnetic dipoles &#8212; commonalites and differences<\/li>\n\n\n\n<li>Magnetization and bound currents<\/li>\n\n\n\n<li>Magnetic field H and magnetic induction B<\/li>\n\n\n\n<li>Scalar magnetic potential<\/li>\n\n\n\n<li>Boundary conditions<\/li>\n\n\n\n<li>Diamagnetism<\/li>\n\n\n\n<li>Paramagnetism<\/li>\n\n\n\n<li>Ferromagnetism<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Current-carrying magnetic slab&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex66.pdf\">[lex66]<\/a><\/li>\n\n\n\n<li>Vector potential of uniformly magnetized sphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex67.pdf\">[lex67]<\/a><\/li>\n\n\n\n<li>Magnetic field of uniformly magnetized sphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex68.pdf\">[lex68]<\/a><\/li>\n\n\n\n<li>Magnetic material between coaxial cylinders with current&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex69.pdf\">[lex69]<\/a><\/li>\n\n\n\n<li>Magnetized material with cavities of different shapes&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex70.pdf\">[lex70]<\/a><\/li>\n\n\n\n<li>Solid sphere placed in a uniform magnetic field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex72.pdf\">[lex72]<\/a>&nbsp;<\/li>\n\n\n\n<li>Magnetic shielding inside a magnetizable spherical shell&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex73.pdf\">[lex73]<\/a><\/li>\n\n\n\n<li>Dynamic response of electric and magnetic moment to torque&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex122.pdf\">[lex122]<\/a><\/li>\n\n\n\n<li>Vector potential generated by magnetic material&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex191.pdf\">[lex191]<\/a><\/li>\n\n\n\n<li>Electric dipole near long electrically charged rod&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex195.pdf\">[lex195]<\/a><\/li>\n\n\n\n<li>Magnetic dipole near long straight current-carrying wire&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex196.pdf\">[lex196]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">8. Electrodynamics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln14.pdf\">[lln14]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Faraday&#8217;s law of electromagnetic induction<\/li>\n\n\n\n<li>Motional EMF<\/li>\n\n\n\n<li>Consistency of motional EMF with Faraday&#8217;s law<\/li>\n\n\n\n<li>Faraday disk generator<\/li>\n\n\n\n<li>Eddy currents and magnetic attenuation<\/li>\n\n\n\n<li>Alternating current generator<\/li>\n\n\n\n<li>Cyclotron<\/li>\n\n\n\n<li>Betatron<\/li>\n\n\n\n<li>Inductance<\/li>\n\n\n\n<li>Self-induction<\/li>\n\n\n\n<li>Energy stored in inductor<\/li>\n\n\n\n<li>Mutual induction<\/li>\n\n\n\n<li>Magnetic field energy density<\/li>\n\n\n\n<li>RL circuits<\/li>\n\n\n\n<li>Electromagnetic oscillator (LC circuit)<\/li>\n\n\n\n<li>LC circuit with two modes<\/li>\n\n\n\n<li>RLC circuit<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Energy dissipation in Faraday disk generator&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex74.pdf\">[lex74]<\/a><\/li>\n\n\n\n<li>Faraday wheel I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex75.pdf\">[lex75]<\/a><\/li>\n\n\n\n<li>Free fall attenuated by eddy current&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex76.pdf\">[lex76]<\/a><\/li>\n\n\n\n<li>Inductance of a toroid&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex77.pdf\">[lex77]<\/a><\/li>\n\n\n\n<li>RL circuit I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex79.pdf\">[lex79]<\/a><\/li>\n\n\n\n<li>RL circuit turning into LC circuit&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex80.pdf\">[lex80]<\/a><\/li>\n\n\n\n<li>Motional EMF I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex81.pdf\">[lex81]<\/a>&nbsp;<\/li>\n\n\n\n<li>Mutual inductance of solenoid and ring&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex86.pdf\">[lex86]<\/a><\/li>\n\n\n\n<li>RC circuit turning into LC circuit&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex87.pdf\">[lex87]<\/a><\/li>\n\n\n\n<li>Circuit breaker contest I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex88.pdf\">[lex88]<\/a><\/li>\n\n\n\n<li>Conducting ring moving into region of magnetic field I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex137.pdf\">[lex137]<\/a><\/li>\n\n\n\n<li>Conducting ring moving into region of magnetic field II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex138.pdf\">[lex138]<\/a>&nbsp;<\/li>\n\n\n\n<li>Circuit breaker contest II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex139.pdf\">[lex139]<\/a><\/li>\n\n\n\n<li>AC circuit with RLC devices in series&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex193.pdf\">[lex193]<\/a>&nbsp;<\/li>\n\n\n\n<li>AC circuits I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex203.pdf\">[lex203]<\/a><\/li>\n\n\n\n<li>AC circuits II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex204.pdf\">[lex204]<\/a><\/li>\n\n\n\n<li>AC circuits III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex205.pdf\">[lex205]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Alternating current circuits&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam28.pdf\">[lam28]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">9. Electrodynamics II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln15.pdf\">[lln15]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Maxwell&#8217;s equations in vacuum<\/li>\n\n\n\n<li>Scalar potential and vector potential<\/li>\n\n\n\n<li>Gauge invariance<\/li>\n\n\n\n<li>Maxwell&#8217;s equations in matter<\/li>\n\n\n\n<li>Path from restricted scenarios toward generality<\/li>\n\n\n\n<li>Poynting theorem<\/li>\n\n\n\n<li>Electromagnetic waves in vacuum<\/li>\n\n\n\n<li>General plane-wave solution<\/li>\n\n\n\n<li>Energy and momentum densities<\/li>\n\n\n\n<li>Spherical wave solution<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Conduction current versus displacement current I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex82.pdf\">[lex82]<\/a><\/li>\n\n\n\n<li>Maxwell&#8217;s equations for scalar and vector potentials&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex83.pdf\">[lex83]<\/a><\/li>\n\n\n\n<li>Vector and scalar potentials of spherical wave&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex84.pdf\">[lex84]<\/a>&nbsp;<\/li>\n\n\n\n<li>Electric and magnetic fields of spherical wave&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex85.pdf\">[lex85]<\/a><\/li>\n\n\n\n<li>Energy delivery into current-carrying wire&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex89.pdf\">[lex89]<\/a>&nbsp;<\/li>\n\n\n\n<li>Longitudinal and transverse current densities&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex134.pdf\">[lex134]<\/a><\/li>\n\n\n\n<li>Scalar and vector potentials in the Coulomb gauge&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex135.pdf\">[lex135]<\/a><\/li>\n\n\n\n<li>Conduction current versus displacement current II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex140.pdf\">[lex140]<\/a>&nbsp;<\/li>\n\n\n\n<li>Circularly polarized plane electromagnetic wave&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex141.pdf\">[lex141]<\/a>&nbsp;<\/li>\n\n\n\n<li>Field energy between capacitor plates I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex142.pdf\">[lex142]<\/a><\/li>\n\n\n\n<li>Field energy inside solenoid I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex143.pdf\">[lex143]<\/a><\/li>\n\n\n\n<li>Maxwell stress tensor for linearly polarized plane wave&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex206.pdf\">[lex206]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">10. Relativity I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln16.pdf\">[lln16]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Postulates of special relativity<\/li>\n\n\n\n<li>Spacetime coordinate transformations<\/li>\n\n\n\n<li>Flash of light expanding<\/li>\n\n\n\n<li>Paradigm shift<\/li>\n\n\n\n<li>Einstein&#8217;s signature clock<\/li>\n\n\n\n<li>Time dilation<\/li>\n\n\n\n<li>Length contraction<\/li>\n\n\n\n<li>Relativity of simultaneity<\/li>\n\n\n\n<li>Time dilation paradox resolved<\/li>\n\n\n\n<li>Length contraction paradox resolved<\/li>\n\n\n\n<li>Addition of velocities<\/li>\n\n\n\n<li>Events and worldlines<\/li>\n\n\n\n<li>Mass and energy<\/li>\n\n\n\n<li>Relativistic momentum<\/li>\n\n\n\n<li>Relativistic energy<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exchange of light signals&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex90.pdf\">[lex90]<\/a><\/li>\n\n\n\n<li>Internal clock of pions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex92.pdf\">[lex92]<\/a>&nbsp;<\/li>\n\n\n\n<li>Jet propulsion&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex93.pdf\">[lex93]<\/a><\/li>\n\n\n\n<li>Photon absorption and photon emission&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex94.pdf\">[lex94]<\/a><\/li>\n\n\n\n<li>Moving calendars&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex144.pdf\">[lex144]<\/a>&nbsp;<\/li>\n\n\n\n<li>Who passes more quickly?&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex145.pdf\">[lex145]<\/a>&nbsp;&nbsp;<\/li>\n\n\n\n<li>Interstellar travel&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex160.pdf\">[lex160]<\/a><\/li>\n\n\n\n<li>Time on the fly&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex161.pdf\">[lex161]<\/a><\/li>\n\n\n\n<li>Interstellar speed control&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex162.pdf\">[lex162]<\/a><\/li>\n\n\n\n<li>Exchange of light signals II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex163.pdf\">[lex163]<\/a><\/li>\n\n\n\n<li>Two events, two views, one common ground&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex164.pdf\">[lex164]<\/a><\/li>\n\n\n\n<li>K meson decay&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex165.pdf\">[lex165]<\/a><\/li>\n\n\n\n<li>Lorentz transformation I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex166.pdf\">[lex166]<\/a><\/li>\n\n\n\n<li>Lorentz transformation II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex167.pdf\">[lex167]<\/a><\/li>\n\n\n\n<li>Observing a rod in transverse motion&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex168.pdf\">[lex168]<\/a><\/li>\n\n\n\n<li>Lorentz invariance of momentum conservation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex169.pdf\">[lex169]<\/a><\/li>\n\n\n\n<li>Relativistic mass from momentum conservation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex170.pdf\">[lex170]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Doppler effect for sound and light&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam22.pdf\">[lam22]<\/a><\/li>\n\n\n\n<li>Skater paradox&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam23.pdf\">[lam23]<\/a><\/li>\n\n\n\n<li>Minkowski diagram&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam24.pdf\">[lam24]<\/a><\/li>\n\n\n\n<li>Twin paradox&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam25.pdf\">[lam25]<\/a><\/li>\n\n\n\n<li>Rapidities&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam26.pdf\">[lam26]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">11. Relativity II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln25.pdf\">[lln25]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Spacetime<\/li>\n\n\n\n<li>Lorentz transformation matrix<\/li>\n\n\n\n<li>Lorentz invariance of 4-vectors<\/li>\n\n\n\n<li>Kinematics<\/li>\n\n\n\n<li>Energy and momentum<\/li>\n\n\n\n<li>Dynamics<\/li>\n\n\n\n<li>Lorentz force and electromagnetic field tensor<\/li>\n\n\n\n<li>Lorentz transformation of electromagnetic field tensor<\/li>\n\n\n\n<li>Partial derivatives Lorentz transformed<\/li>\n\n\n\n<li>Current 4-vector and continuity equation<\/li>\n\n\n\n<li>Maxwell&#8217;s equations in covariant form<\/li>\n\n\n\n<li>Lorentz invariance of Maxwell equations<\/li>\n\n\n\n<li>4-vector potential<\/li>\n\n\n\n<li>Summary list of Lorentz transformations<\/li>\n\n\n\n<li>Electromagnetic wave observed in moving frames<\/li>\n\n\n\n<li>Energy-momentum flux tensor<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Velocity addition rule from principle of relativity&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex91.pdf\">[lex91]<\/a><\/li>\n\n\n\n<li>Fields between moving capacitor plates I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex95.pdf\">[lex95]<\/a>&nbsp;<\/li>\n\n\n\n<li>Point charge in uniform motion I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex96.pdf\">[lex96]<\/a><\/li>\n\n\n\n<li>Fields between moving capacitor plates II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex146.pdf\">[lex146]<\/a><\/li>\n\n\n\n<li>Lorentz invariance of Maxwell&#8217;s equations&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex194.pdf\">[lex194]<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">12. Optics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln17.pdf\">[lln17]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Electromagnetic wave in dielectric<\/li>\n\n\n\n<li>Reflection and refraction at plane dielectric interface<\/li>\n\n\n\n<li>Total internal reflection<\/li>\n\n\n\n<li>Normal-incidence reflectivity<\/li>\n\n\n\n<li>Nonreflecting surface via dielectric coating<\/li>\n\n\n\n<li>Plane-wave incidence at an angle<\/li>\n\n\n\n<li>Reflection and refraction of TE plane wave<\/li>\n\n\n\n<li>Reflection and refraction of TM plane wave<\/li>\n\n\n\n<li>Brewster angle<\/li>\n\n\n\n<li>Energy conservation<\/li>\n\n\n\n<li>Electromagnetic waves in a conductor<\/li>\n\n\n\n<li>Reflection from conductor<\/li>\n\n\n\n<li>Dispersion<\/li>\n\n\n\n<li>Dispersion in a dielectric<\/li>\n\n\n\n<li>Dispersion in a plasma<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Anti-reflection coating&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex97.pdf\">[lex97]<\/a><\/li>\n\n\n\n<li>Fresnel equation for TE wave&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex98.pdf\">[lex98]<\/a><\/li>\n\n\n\n<li>Fresnel equation for TM wave&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex99.pdf\">[lex99]<\/a><\/li>\n\n\n\n<li>Electromagnetic wave in a conductor&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex100.pdf\">[lex100]<\/a><\/li>\n\n\n\n<li>Reflection of electromagnetic wave from a conductor&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex101.pdf\">[lex101]<\/a><\/li>\n\n\n\n<li>Driven harmonic oscillator: steady-state solution&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex102.pdf\">[lex102]<\/a><\/li>\n\n\n\n<li>Dispersion and absorption in a dielectric&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex103.pdf\">[lex103]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">13. Optics II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln18.pdf\">[lln18]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Electromagnetic wave between parallel conducting plates<\/li>\n\n\n\n<li>Transverse electric and magnetic (TEM) wave<\/li>\n\n\n\n<li>Transverse electric (TE) wave<\/li>\n\n\n\n<li>Energy transport in TE wave<\/li>\n\n\n\n<li>Geometrical interpretation of phase\/group velocities<\/li>\n\n\n\n<li>Transverse magnetic (TM) wave<\/li>\n\n\n\n<li>Energy transport in TM wave<\/li>\n\n\n\n<li>Rectangular wave guide<\/li>\n\n\n\n<li>TE modes in rectangular wave guide<\/li>\n\n\n\n<li>TM modes in rectangular wave guide<\/li>\n\n\n\n<li>Wave guide with cross section of arbitrary shape<\/li>\n\n\n\n<li>TE modes in wave guides of arbitrary cross section<\/li>\n\n\n\n<li>TM modes in wave guides of arbitrary cross section<\/li>\n\n\n\n<li>Conditions for TEM modes in wave guides of arbitrary cross section<\/li>\n\n\n\n<li>TEM mode in coaxial cable<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TE mode in rectangular wave guide&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex104.pdf\">[lex104]<\/a><\/li>\n\n\n\n<li>Surface charge and current in rectangular wave guide I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex105.pdf\">[lex105]<\/a><\/li>\n\n\n\n<li>Surface charge and current in rectangular wave guide II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex106.pdf\">[lex106]<\/a><\/li>\n\n\n\n<li>Helmholtz equation for wave guide I: TE modes&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex107.pdf\">[lex107]<\/a><\/li>\n\n\n\n<li>Helmholtz potential for wave guide II: TM modes&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex108.pdf\">[lex108]<\/a><\/li>\n\n\n\n<li>TEM mode in coaxial cable I: electric and magnetic fields&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex109.pdf\">[lex109]<\/a><\/li>\n\n\n\n<li>TEM mode in coaxial cable II: impedance&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex110.pdf\">[lex110]<\/a><\/li>\n\n\n\n<li>Phase velocity and group velocity&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex172.pdf\">[lex172]<\/a>&nbsp;<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">14. Radiation I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln19.pdf\">[lln19]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Retarded potentials<\/li>\n\n\n\n<li>Radiation from electric dipole<\/li>\n\n\n\n<li>Hertzian dipole (special case)<\/li>\n\n\n\n<li>Radiation from magnetic dipole<\/li>\n\n\n\n<li>Electric dipole radiation at arbitrary distance<\/li>\n\n\n\n<li>Half-wave linear antenna<\/li>\n\n\n\n<li>Radiation from an accelerated charged particle<\/li>\n\n\n\n<li>Light scattering from bound charged particle<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Green&#8217;s function of&nbsp;\u22072+k2&nbsp;&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex111.pdf\">[lex111]<\/a>&nbsp;<\/li>\n\n\n\n<li>Planar surface current abruptly established&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex112.pdf\">[lex112]<\/a><\/li>\n\n\n\n<li>Electric dipole moment from charge density or current density&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex113.pdf\">[lex113]<\/a><\/li>\n\n\n\n<li>Magnetic radiation field of electric dipole&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex114.pdf\">[lex114]<\/a><\/li>\n\n\n\n<li>Electric radiation field of electric dipole&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex115.pdf\">[lex115]<\/a><\/li>\n\n\n\n<li>Poynting vector and radiation power of electric dipole&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex116.pdf\">[lex116]<\/a><\/li>\n\n\n\n<li>Antenna resistance of Hertzian dipole&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex117.pdf\">[lex117]<\/a><\/li>\n\n\n\n<li>Radiation fields an Poynting vector for half-wave linear antenna&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex118.pdf\">[lex118]<\/a><\/li>\n\n\n\n<li>Larmor formula for radiation of accelerated charged particle&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex119.pdf\">[lex119]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">15. Magnetism I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln22.pdf\">[lln22]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angular momentum of electrons<\/li>\n\n\n\n<li>Two-electron wave function<\/li>\n\n\n\n<li>Atomic electrons in a magnetic field<\/li>\n\n\n\n<li>Diamagnetism<\/li>\n\n\n\n<li>Langevin and Brillouin paramagnetism<\/li>\n\n\n\n<li>Van Vleck paramagnetism<\/li>\n\n\n\n<li>Fine structure<\/li>\n\n\n\n<li>Hund&#8217;s rule<\/li>\n\n\n\n<li>Russell-Saunders coupling<\/li>\n\n\n\n<li>Land\u00e9 g-factor<\/li>\n\n\n\n<li>Nuclear spins<\/li>\n\n\n\n<li>Hyperfine structure<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Diamagnetic response of electron in circular orbit&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex121.pdf\">[lex121]<\/a><\/li>\n\n\n\n<li>Dynamic response of electric and magnetic moment to torque&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex122.pdf\">[lex122]<\/a><\/li>\n\n\n\n<li>Hyperfine-coupling Hamiltonian&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex123.pdf\">[lex123]<\/a>&nbsp;<\/li>\n\n\n\n<li>Magnetic ground state of some Lanthanide ions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex173.pdf\">[lex173]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">16. Magnetism II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln23.pdf\">[lln23]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Crystal field<\/li>\n\n\n\n<li>Low-field and high-field regimes<\/li>\n\n\n\n<li>Orbital quenching<\/li>\n\n\n\n<li>Jahn-Teller effect<\/li>\n\n\n\n<li>Nuclear magnetic resonance<\/li>\n\n\n\n<li>Bloch equations<\/li>\n\n\n\n<li>Electron spin resonance<\/li>\n\n\n\n<li>M\u00f6ssbauer spectroscopy<\/li>\n\n\n\n<li>Muon-spin rotation<\/li>\n\n\n\n<li>Exchange interaction<\/li>\n\n\n\n<li>Mediated exchange interaction<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Level populations and rate of energy absorption in NMR [<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex171.pdf\">lex171]<\/a><\/li>\n\n\n\n<li>Bloch equations I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex174.pdf\">[lex174]<\/a><\/li>\n\n\n\n<li>Bloch equations II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex175.pdf\">[lex175]<\/a><\/li>\n\n\n\n<li>Exchange integral&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex176.pdf\">[lex176]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">17. Quantum Optics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln24.pdf\">[lln24]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Levels of quantization<\/li>\n\n\n\n<li>Blackbody radiation<\/li>\n\n\n\n<li>Einstein coefficients<\/li>\n\n\n\n<li>Radiative transition rates<\/li>\n\n\n\n<li>Linewidth and lineshape<\/li>\n\n\n\n<li>Photon statistics<\/li>\n\n\n\n<li>Light with Poisson statistics<\/li>\n\n\n\n<li>Light with Pascal statistics<\/li>\n\n\n\n<li>Light with super-Poisson statistics<\/li>\n\n\n\n<li>Light with sub-Poisson statistics<\/li>\n\n\n\n<li>Statistics of photon number states<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mean and variance of Poisson distribution&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex149.pdf\">[lex149]<\/a><\/li>\n\n\n\n<li>Mean and variance of Pascal distribution&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex150.pdf\">[lex150]<\/a><\/li>\n\n\n\n<li>Erlang distributions I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex151.pdf\">[lex151]<\/a><\/li>\n\n\n\n<li>Erlang distributions II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex152.pdf\">[lex152]<\/a><\/li>\n\n\n\n<li>Photon statistics from Planck&#8217;s radiation law&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex153.pdf\">[lex153]<\/a><\/li>\n\n\n\n<li>Super-Poisson interpolation statistics I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex177.pdf\">[lex177]<\/a><\/li>\n\n\n\n<li>SuperPoisson intepolation statistics II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex178.pdf\">[lex178]<\/a><\/li>\n\n\n\n<li>Differential recursion relation or Poisson and Pascal statistics&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex179.pdf\">[lex179]<\/a><\/li>\n\n\n\n<li>Photon detection events from thermal radiation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex180.pdf\">[lex180]<\/a>&nbsp;<\/li>\n\n\n\n<li>Poisson distribution from maximizing uncertainty&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex181.pdf\">[lex181]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">18. Quantum Optics II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln26.pdf\">[lln26]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Photon bunching and antibunching<\/li>\n\n\n\n<li>Light modeled as harmonic oscillations<\/li>\n\n\n\n<li>Phasor diagram and field quadratures<\/li>\n\n\n\n<li>Coherent states of light<\/li>\n\n\n\n<li>Squeezed states of light<\/li>\n\n\n\n<li>Criteria for the classification of light<\/li>\n\n\n\n<li>Photonic number states<\/li>\n\n\n\n<li>Photonic coherent states<\/li>\n\n\n\n<li>Photonic thermal states<\/li>\n\n\n\n<li>Phase-space representations of photonic states<\/li>\n\n\n\n<li>Intensity correlations of photonic number states<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coherent state of quantum harmonic oscillator I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex154.pdf\">[lex154]<\/a><\/li>\n\n\n\n<li>Coherent state of quantum harmonic oscillator II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex155.pdf\">[lex155]<\/a><\/li>\n\n\n\n<li>Position distribution in harmonic oscillator&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex182.pdf\">[lex182]<\/a><\/li>\n\n\n\n<li>Quantum uncertainty in ground state of harmonic oscillator&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex183.pdf\">[lex183]<\/a>&nbsp;<\/li>\n\n\n\n<li>Phase-space distribution in harmonic oscillator&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex184.pdf\">[lex184]<\/a><\/li>\n\n\n\n<li>Coherent state of quantum harmonic oscillator III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex185.pdf\">[lex185]<\/a><\/li>\n\n\n\n<li>Mixed versus pure photonic states&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex186.pdf\">[lex186]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Density operator&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam1.pdf\">[lam1]<\/a><\/li>\n\n\n\n<li>First- and second-order correlation functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam2.pdf\">[lam2]<\/a><\/li>\n\n\n\n<li>Quantization of the electromagnetic field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam3.pdf\">[lam3]<\/a><\/li>\n\n\n\n<li>Uncertainty&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam4.pdf\">[lam4]<\/a>&nbsp;<\/li>\n\n\n\n<li>Quantum harmonic oscillator&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam5.pdf\">[lam5]<\/a>&nbsp;<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">19. Quantum Optics III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lln27.pdf\">[lln27]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Resonant light-atom interactions<\/li>\n\n\n\n<li>Pure versus mixed quantum states<\/li>\n\n\n\n<li>Bloch sphere<\/li>\n\n\n\n<li>Schr\u00f6dinger equation of interacting system<\/li>\n\n\n\n<li>Einstein coefficients in the weak-field limit<\/li>\n\n\n\n<li>Rabi oscillations in the strong-field limit<\/li>\n\n\n\n<li>Optical cavities<\/li>\n\n\n\n<li>Two-level atom in optical cavity<\/li>\n\n\n\n<li>Weak-coupling regime<\/li>\n\n\n\n<li>Purcell effect<\/li>\n\n\n\n<li>Strong-coupling regime<\/li>\n\n\n\n<li>Cold atoms from laser cooling<\/li>\n\n\n\n<li>Optical molasses<\/li>\n\n\n\n<li>Doppler limit for laser cooling<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rabi oscillations off resonance&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex156.pdf\">[lex156]<\/a><\/li>\n\n\n\n<li>Einstein coefficients for hydrogen 1s&nbsp;\u21922p transition&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex157.pdf\">[lex157]<\/a><\/li>\n\n\n\n<li>Einstein coefficients for hydrogen 2s&nbsp;\u21923p transition&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex158.pdf\">[lex158]<\/a><\/li>\n\n\n\n<li>Jaynes Cummings model I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/wlex159.pdf\">[lex159]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Additional Materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Quantum time evolution and measurement&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY331N\/lam6.pdf\">[lam6]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p><small><strong>Some Relevant Textbooks and Monographs:<\/strong><\/small><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>R. H. Good:&nbsp;<em>Classical Electromagnetism<\/em>. Saunders, 1999.<\/li>\n\n\n\n<li>D. J. Griffiths:&nbsp;<em>Introduction to Electrodynamics<\/em>. Prentice Hall,&nbsp; 1999.<\/li>\n\n\n\n<li>J. D. Jackson: Classical&nbsp;<em>Electrodynamics<\/em>&nbsp;(3rd Ed.) Wiley, New York 1999.<\/li>\n\n\n\n<li>G. L. Pollack and D. R. Stump:&nbsp;<em>Electromagnetism<\/em>. Addison Wesley, San Francisco 2002.<\/li>\n\n\n\n<li>J. R. Reitz, F. J. Milford, and R. W. Christy:&nbsp;<em>Foundations of Electromagnetic Theory<\/em>. Addison Wesley, 1993<\/li>\n\n\n\n<li>S. Blundell:&nbsp;<em>Magnetism in Condensed Matter<\/em>. Oxford University Press 2011.<\/li>\n\n\n\n<li>M. Fox:&nbsp;<em>Quantum Optics<\/em>. Oxford University Press 2014.<\/li>\n\n\n\n<li>P. Lambropoulos and D. Petrosyan:&nbsp;<em>Fundamentals of Quantum Optics and Quantum Information<\/em>. Springer, 2007<\/li>\n\n\n\n<li>R. Wald:&nbsp;<em>Advanced Classical Electromagnetism<\/em>. Princeton University Press 2022.<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p><br><small>Last updated 08\/31\/23<\/small><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Teaching PHY331|PHY510 |PHY525 &nbsp; This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Electricity and Magnetism This topic outline is incomplete in many respects. Updates are being posted periodically. These lecture notes are for&nbsp;the advanced undergraduate course PHY331 and for the graduate courses PHY530\/PHY630. In PHY331 the goal is cover parts of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-twocol.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-420","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages\/420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/comments?post=420"}],"version-history":[{"count":19,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages\/420\/revisions"}],"predecessor-version":[{"id":528,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages\/420\/revisions\/528"}],"wp:attachment":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/media?parent=420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}