{{page>wiki:headers:hheader}} ==== Unit: Gauss's Law ==== === Flux (20-50 minutes)=== * [[..:prereq:vfpre:vfpreflux|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:flux|Flux]]--[[bb>book:physics:cubehint|More Flux through a Cube]] * [[swbq:vcsw:vfswflux|Recall Flux]] (SWBQ) //5 min// * [[..:activities:vfact:vffluxconcept|The Concept of Flux]] (Kinesthetic Activity) //5 min// * [[..:activities:vfact:vffluxcalculation|Calculating Flux]] (Small Group Activity--Optional) //30 min// * [[..:activities:vfact:vffluxem|Visualizing Electric Flux]] (Maple) //10 min// - plots electric field vectors from a charge in a box and calculates the flux through the surfaces of the box. Leads to a statement of Gauss' law. * [[..:lecture:vflec:vflecflux|Flux]] (Lecture, if necessary) Fill in any holes not covered by the activities and class discussions. * [[..:hw:vfhw:vfhwflux|Homework]] === Gauss's Law (120 minutes)=== * [[..:prereq:vfpre:vfpregauss|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:physics:gausssymmetry|Gauss's Law and Symmetry]]--[[bb>book:physics:gaussacthint|More Gauss's Law: Cylinders and Spheres]] * [[..:lecture:vflec:vflecgauss|Gauss' Law -- the integral version]] (Lecture) //30 min// * [[..:activities:vfact:vfgauss|Gauss' Law]] (SGA) //90 min// - students solve for the electric field due to a charged sphere or an infinite cylinder. Emphasis is made on students making symmetry arguments (proof by contradiction) for using Gauss' Law. * [[..:hw:vfhw:vfhwgauss|Homework]] === Divergence (40 min) === * [[..:prereq:vfpre:vfprediv|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:divergence|Definition of Divergence]]--[[bb>book:math:divcoord|Divergence in Curvlinear Coordinates]],[[bb>book:physics:divact|Visualizing Divergence]]--[[bb>book:physics:divacthint|More Visualizing Divergence]] * Definition of divergence (Lecture) //20 min// * [[..:activities:vfact:vfdivergence|Visualizing Divergence]] (Maple Visualization) //20 min// Students practice estimating divergence from graphs of various vector fields. * [[..:hw:vfhw:vfhwdiv|Homework]] === Divergence Theorem (20 min) === * [[..:prereq:vfpre:vfpredivthm|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:divthm|Divergence Theorem]] * Derivation of the Divergence Theorem (lecture). We follow "div, grad, curl and all that", by Schey. The Divergence theorem is almost a lemma based on the definition of divergence. Draw a diagram of an arbitrary volume divided into lots of little cubes. Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary. * [[..:hw:vfhw:vfhwdivthm|Homework]] === Differential Form of Gauss's Law (10 min) === * [[..:prereq:vfpre:vfpredifgauss|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:physics:maxwell1|Differential Form of Gauss's Law]]--[[bb>book:physics:lines|Electric Field Lines]] * Differential Form of Gauss's Law: Maxwell's Eq 1 & 3: $\Vec{\nabla} \cdot \Vec{E} = {\rho \over \epsilon_0}$, $\Vec{\nabla~} \cdot \Vec{B} = 0$ (lecture) * (//optional//) Divergence of a Coulomb field (//requires delta functions//) (lecture) * (//optional//) Electric field lines (lecture) * [[..:hw:vfhw:vfhwgsslawdiff|Homework]] ==== Unit: Current, Magnetic Vector Potential, and Magnetic Field ==== === Current === * [[..:prereq:vfpre:vfprecurrentden|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:physics:currents|Currents]] * [[..:activities:vfact:vfcurrentdensity|Acting Out Current Density]] (kinesthetic) * Current Density (lecture) //10 min// * [[..:hw:vfhw:vfhwcurrentden|Homework]] === Vector Potentials (Optional) === * [[..:prereq:vfpre:vfprevectorpot|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:physics:vpot|Magnetic Vector Potential]]--[[bb>book:math:curl2|Curl]] * Vector Potential A (lecture) //10 min max// This can be just an analogy with electrostatic potential. * [[..:activities:vfact:vfaring|Magnetic Vector Potential Due to a Spinning Ring of Charge]] (SGA) * Curl (at least the component definition in rectangular coordinates) * [[..:hw:vfhw:vfhwvectpot|Homework]] === Magnetic Fields === * [[..:prereq:vfpre:vfpremagfield|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:physics:bs|Derivation of the Biot Savart Law from Magnetic Vector Potential]]--[[bb>book:physics:compareab|Compare A and B for a Spinning Ring]] * Derivation of the Biot-Savart Law from Magnetic Vector Potential (lecture) //15 min// * [[..:activities:vfact:vfbring|Magnetic Field Due to a Spinning Ring of Charge]] (SGA) * (//optional//) Comparing B and A for spinning ring (class discussion/lecture) * [[..:hw:vfhw:vfhwbiot|Homework]] ==== Unit: Ampère's Law ==== === Ampère's Law === * [[..:prereq:vfpre:vfpreampere|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:physics:bplane|The Magnetic Field of a Uniform Planar Current]] [[bb>book:physics:ampere|Ampère's Law and Symmetry]] * [[..:lecture:vflec:vflecampere|Ampère's Law and Symmetry Argument]] (Lecture) //20 min// * [[..:activities:vfact:vfampere|Ampère's Law]] (SGA) * [[..:hw:vfhw:vfhwampere|Homework]] === Curl === * [[..:prereq:vfpre:vfprecurl|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:lineintv|Vector Line Integrals]]--[[bb>book:math:drpath|Use What You Know]],[[bb>book:math:curl2|Definition of Curl]] * Circulation (lecture) * [[..:activities:vfact:vfcurlvis|Visualizing Curl]] (Maple) * Definition of Curl (lecture). We follow "div, grad, curl and all that", by Schey * [[..:hw:vfhw:vfhwcurl|Homework]] === Stokes' Theorem === * [[..:prereq:vfpre:vfprestokes|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:stokes|Stokes' Theorem]] * Derivation of Stokes' Theorem (lecture). We follow "div, grad, curl and all that", by Schey * [[..:hw:vfhw:vfhwstokes|Homework]] === Differential Form of Ampère's Law === * [[..:prereq:vfpre:vfprediffamp|Prerequisite Ideas]] * Stokes' Theorem (lecture) (//Math 3.12: Stokes' Theorem//) * Differential Form of Ampère's Law: Maxwell Eq. 2 & 4 $\Vec{\nabla~} \times \Vec{E} = 0$, $\Vec{\nabla~} \times \Vec{B} = \mu_0 \Vec{J}$(lecture) (//Physics 41: Differential Form of Ampère's Law//) * [[..:hw:vfhw:vfhwdiffamp|Homework]] ==== Unit: Conductors ==== === Step & Delta Functions (1 hr) === * [[..:prereq:vfpre:vfprestepdelta|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:step|Step Functions]]--[[bb>book:math:deltadensity|The Dirac Delta Function and Densities]] * Step Functions * Delta Functions * [[..:hw:vfhw:vfhwthetadelta|Homework]] === Conductors (1 hr) === * [[..:prereq:vfpre:vfpreconductors|Prerequisite Ideas]] * [[..:hw:vfhw:vfhwpreconductors|Prerequisite Homework]] * Conductors (lecture) * [[..:activities:vfact:vfconductors|Conductors]] (SGA) * [[..:hw:vfhw:vfhwconductors|Homework]] === Boundary Conditions === * [[..:prereq:vfpre:vfprebc|Prerequisite Ideas]] * [[..:activities:vfact:vfebound|Continuity of the Electric Field at Boundaries]] (SGA) * [[..:activities:vfact:vfbbound|Continuity of the Magnetic Field at Boundaries]] (SGA) ==== Unit: Conservative Fields ==== === Conservative Fields === * [[..:prereq:vfpre:vfpreconservative|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:path|Independence of Path]]--[[bb>book:math:mmm|Finding potential Functions]] * Conservative Fields (lecture) (//Math 3.5: Independence of Path//, //Math 3.6: Conservative Vector Fields//, //Math 3.7: Finding Potential Functions//) * [[..:activities:vfact:vfmurdermm|Murder Mystery Method]] (SGA) * Equivalent Statements (lecture) * [[..:hw:vfhw:vfhwmmm|Homework]] === Second Derivatives === * [[..:prereq:vfpre:vfpre2ndderivs|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:second|Second Derivatives]],[[bb>book:math:laplacian|The Laplacian]] * Second Derivatives & the Laplacian (lecture) * (//optional//) [[..:activities:vfact:vflaplacerelax|Relaxation Technique for Solving Laplace's Equation]] (SGA) ==== Unit: Energy ==== === Product Rules === * [[..:prereq:vfpre:vfpreproductrules|Prerequisite Ideas]] * Reading: GVC (ss) [[bb>book:math:rules|Product Rules]]--[[bb>book:math:parts|Integration by Parts]] * Product Rules (lecture) * Integration by Parts (lecture) === Energy for Continuous Distributions === * [[..:prereq:vfpre:vfpreemenergy|Prerequisite Ideas]] * Energy for Continuous Distributions (lecture) * [[..:hw:vfhw:vfhwemenergy|Homework]]