{{page>wiki:headers:hheader}} ==== Unit: Potentials from Discrete Sources ==== [[http://www.math.hmc.edu/calculus/tutorials/|Some nice review tutorials from Harvey Mudd College]] : **Hour 1: [[..:order20:vforder20:vfpotential1|Electric Potential]] ** * QUIZ * Coulomb's Law : **Hours 2-3: [[..:order20:vforder20:vfpotential2|Potential Due to Point Charges]] ** * Superposition * //Small Group Activity: Visualizing Equipotential Surfaces// * Equipotential surfaces : **Hour 4: [[..:order20:vforder20:vfpowerseries|Power Series]] ** This hour is likely to move to Energy and Entropy in the future. * Power Series Approximations * //Small Group Activity: Calculating Coefficients for a Power Series// * Properties of Power Series : **Hour 5: [[..:order20:vforder20:vfdistance|The Distance between Two Points]] ** * Vectors * //Kinesthetic Activity: Star Trek// * Dot Products : **Hour 6: [[..:order20:vforder20:vftwopc|Two Point Charges]] ** * Dipoles * //Small Group Activity: Electric Potential for 2 Point Charges (with Power Series)// : **Hour 7: [[..:order20:vforder20:vfdrvector|Differential Vector Elements]] ** Math Bits?? * The Position Vector * The //dr// Vector * //Small Group Activity: Vector Differentials// ==== Unit: Continuous Charge Distributions ==== : **Hour 8: [[..:order20:vforder20:vflineint|Line Integrals]] ** Math Bits?? * QUIZ * Line Integrals * //Small Group Activity: Boysenberry Patch// : **Hours 9-10: [[..:order20:vforder20:vfintegrating|Integrating Charge Densities]] ** Math Bits?? * Charge Density * //Kinesthetic Activity: Acting Out Charge Densities// * Cross Product * //Small Group Activity: Finding dA and dV// * Total Charge * //Small Group Activity: Total Charge// ==== Unit: Potentials Due to Continuous Distributions ==== : **Hours 11-12: [[..:order20:vforder20:vfcalculating|Calculating Potentials]] ** *Find the surface area of a cone *SQBQ write $d\vec r$ in 3 different coordinate systems * ------ Old ------ * Potential Integrals * //Small Group Activity: The Ring 1 (V)// * Approximating Integrals with Power Series * Potential Due to Finite and Infinite Lines : **Hours 13-14: [[..:order20:vforder20:vfdrawfield|Superposition of Electric Fields]] ** * Electric Field Vectors * //Small Group Activity: The Ring 2 (E)// ==== Unit: Derivatives of Fields ==== : **Hour 15-16: [[..:order20:vforder20:vfgradient|Gradient]] ** Math Bits?? * QUIZ * The Gradient * //Surfaces Activity: The Hillside// * //Small Group Activity: Navigating a Hill// * //Kinesthetic Activity: Acting out the Gradient// * Directional Derivatives (Optional) * Electric Field as Gradient : **Hour 17: [[..:order20:vforder20:vfflux|Flux]] ** * Electric Flux * //Kinesthetic Activity: The Concept of Flux// * //Small Group Activity: Calculating Flux// * //Mathematica Activity: Visualizing Electric Flux// : **Hour 18: [[..:order20:vforder20:vfdivergence|Divergence]] ** Math Bits?? * The Divergence * //Small Group Activity: Visualizing Divergence// * The Divergence Theorem * Gauss's Law (Differential Form) : **Hours 19-20: [[..:order20:vforder20:vfgauss|Gauss's Law]] ** * Gauss's Law (Integral Form) * //Small Group Activity: Using Gauss's Law// : **Hours 21-22: [[..:order20:vforder20:vfconservative|Conservative Fields]] ** * What Fields Are Conservative? * //Small Group Activity: Counting Paths// * Vector line integrals * QUIZ * Relating Work to Potential * //Small Group Activity: Work// FIXME * Finding Potentials from Fields * //Small Group Activity: The Murder Mystery Method// ==== Unit: Laplace's Equation ==== : **Hours 23-25: [[..:order20:vforder20:vflaplace|Solving Laplace's Equation]] ** * Second Derivatives * The Laplacian * Conductors * Separation of Variables * //Small Group Activity: Boundary Value Problem// (New activity) * //Computer Activity: Relaxation Technique// (Optional/Computation course) ==== Unit: Electrostatic Energy ==== : **Hour 26: [[..:order20:vforder20:vfenergy|Energy]] ** * Electrostatic Energy * //Kinesthetic Activity: Energy of Discrete Charges// ==== Unit: Current, Magnetic Vector Potential, and Magnetic Field ==== : **Hour 27: [[..:order20:vforder20:vfcurl|Curl]] ** Math Bits?? * The Curl as Circulation * //Small Group Activity: Visualizing Curl// * The Curl in Curvilinear Coordinates : **Hour 28: [[..:order20:vforder20:vfcurrent|Current]] ** * Electric Current * Current Density * //Kinesthetic Activity: Acting Out Current Density// : **Hours 29-30: [[..:order20:vforder20:vfvectorpot|Vector Potentials]] ** * QUIZ * What Is Vector Potential? * //Small Group Activity: The Ring 3 (A)// : **Hours 31-32: [[..:order20:vforder20:vfmagnetic|Magnetic Fields]] ** * The Biot-Savart Law * //Small Group Activity: The Ring 4 (B)// ==== Unit: Ampère's Law ==== : **Hour 33: [[..:order20:vforder20:vfampere|Ampère's Law]] ** * Symmetry Arguments * //Small Group Activity: Ampère's Law// : **Hour 34: [[..:order20:vforder20:vfstokes|Stokes' Theorem]] ** * Curl Revisited * Stokes' Theorem * //Small Group Activity: Where Is the Current?//FIXME We need a new activity : **Hour 35: Review** ===== Related Topics Not Currently Included ===== ==== Unit: Conductors ==== === Step & Delta Functions (1 hr) === Note that this is now covered in Waves and Oscillations, and also in Periodic Systems * [[..: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]] === Boundary Conditions === These feel like they go really well early in the Capstone to set up E and B fields in matter. * [[..: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) === 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]]