1 / 13

PHY 417G: Review

This review explores the fundamental concepts of classical electromagnetic field theory and its applications in physics. Topics include action at a distance versus locality, the role of fields in carrying forces, the extension of these concepts to quantum field theories, and the omnipresence and differentiability of electromagnetic fields. The review also covers boundary value problems, partial differential equations, and the solution to physical problems in electromagnetic field theory.

caseym
Download Presentation

PHY 417G: Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PHY 417G: Review Christopher Crawford 2015-04-29

  2. Classical Electromagnetic Field • action at a distance vs. locality • field ”mediates “carries force • extends to quantum field theories • field is everywhere always E (x, t) • differentiable, integrable • field lines, equipotentials • PDE – boundary value problems • solution to physical problems

  3. Boundary Value Problem (BVP) • Partial Differential Equation (PDE) BULK • Represents the physics of continuous media • General solution by separation of variables • Linear equation –> inf. dim. linear solution function space • Boundary Conditions (BC) SURFACE Use orthogonality to calculate components of gen. solution Interior BCs – continuity • Derives directly from the PDE Exterior BCs – physics input • Uniqueness theorem: one BC per surface (elliptic) 1 or 2 initial conditions (diffusion, hyperbolic wave) • Now we just have to know the PDE to solve!

  4. Magnetic scalar potential Electrostatics – Coulomb’s law Magnetostatics – Biot-Savart law B.C.’s:Flux lines bounded by charge Flux lines continuous Flow sheets continuous (equipotentials) Flow sheets bounded by current

  5. L/T separation of E&M fields

  6. Formulations of E & M PDEs • Electricity Magnetism • Note the interchange of flux and flow: twisted symmetry!

  7. Electrodynamics • Faraday’s law: 3rd experimental law • Motional EMF equivalent to truly moving or changing magnetic field • Basis of special relativity – electromagnetic field F = E dt + B • 3“Ampère’s Laws”: H(J), A(B), E(eB/dt) • 3+1 lumped components: capacitor, resistor, inductor (reluctance) • Maxwell’s displacements current: theoretical prediction • Relativistic complete derivative chain: gauge, potential, fields, current • Completes Maxwell equations – PDE’s of electrodynamics • Macroscopic equations: 3 charges + 5 currents • We could go back and create 5 formulations of electrodynamics: • I) Jefimenko’s eqs, II+III) Maxwell’s integral/differential equationsIV) Retarded potential: Green’s function of V) WAVE EQUATION

  8. Polarization & Magnetization • Chapter 4: electric materials –> Chapter 6: magnetic materials • Polarization chain –> Magnetization mesh

  9. 3 Materials –> 3 Components • Materials constants: permittivity, resistivity, permeability • Electrical components: capacitor, resistor, inductor • Each is a ratio of Flux / Flow !

  10. Equations of Electrodynamics

  11. Dynamics of E&M • Maxwell’s equations – dynamics of the field • Source equations – charge(ρ,J)generates the E&M field • Force equations – nature of E&M force: conservation of (E,p) • Lorentz Force equation – dynamics of charged particles • Additional equation independent of Maxwell eq’s. • Integrate to get energyE=Fdx, momentump=Fdt, • Conserved currents • Charge (current density) • Energy (Poynting vector) • Momentum (stress tensor) • Conservation principles can be used to simplify problems

  12. Electromagnetic waves • Homogeneous wave equation – Helmholtz equation • Separation of variables / eigenfunctions: Exp, Legendre, Bessel • 3 material properties (ε, μ, σ) –> 2 complex medium properties • Dispersion relationk(ω): propagation (attenuation, wavelength) • Characteristic ImpedanceZ(ω): boundary (reflection, phase shift) • Boundary value problems • Across an interface: Fresnel coefficientsreflection / transmission [impedance] • Along a wave guide: modes of propagation standing transverse waves, kt2 affects dispersion relation • Examples of waves • 1-d: String wave, telegrapher’s equations • 2-d: Surface waves, gravity waves, transverse waveguide modes • 3-d: Seismic/acoustic waves, electromagnetic waves

  13. Final exam: • Integration • Biot-Savart, vector potential • Ampère’s law H(J), Potential A(B), Faraday’s law E(dB/dt) • Calculation of Resistance, Inductance, Reluctance • Dynamics and Conservation • Derivation of magnetic formulations, potentials, wave equations • Derivation of conservation principles: charge, energy, momentum • Boundary value problems • Magnetostatic with materials • Interface reflection/transmission • Waveguide modes • Essay questions – long and short • Flux, flow, Maxwell equations, displacement currents, waves • Properties of materials: magnetization, dispersion, impedance

More Related