ECE Engineering Model

of 39 /39
1 ECE Engineering Model The Basis for Electromagnetic and Mechanical Applications Horst Eckardt, AIAS Version 4.1, 11.1.2014

Embed Size (px)

description

ECE Engineering Model. The Basis for Electromagnetic and Mechanical Applications Horst Eckardt, AIAS. Version 4.1, 11.1.2014. ECE Field Equations. Field equations in tensor form With F: electromagnetic field tensor, its Hodge dual, see later J: charge current density - PowerPoint PPT Presentation

Transcript of ECE Engineering Model

  • *ECE Engineering ModelThe Basis for Electromagnetic and Mechanical Applications

    Horst Eckardt, AIASVersion 4.1, 11.1.2014

  • *ECE Field EquationsField equations in tensor form

    WithF: electromagnetic field tensor, its Hodge dual, see laterJ: charge current densityj: homogeneous current density, magnetic currenta: polarization index,: indexes of spacetime (t,x,y,z)

  • *Properties of Field EquationsJ is not necessarily external current, is defined by spacetime properties completelyj only occurs if electromagnetism is influenced by gravitation, or magnetic monopoles exist, otherwise =0Polarization index a can be omitted if tangent space is defined equal to space of base manifold (assumed from now on)

  • *Electromagnetic Field TensorF and are antisymmetric tensors, related to vector components of electromagnetic fields (polarization index omitted)Cartesian components are Ex=E1 etc.

  • *Potential with polarization directionsPotential matrix:

    Polarization vectors:

  • *ECE Field Equations Vector FormMaterial EquationsDielectric DisplacementMagnetic Induction

  • *Physical UnitsCharge Density/CurrentMagnetic Density/Current

  • *Field-Potential Relations IFull Equation SetPotentials and Spin ConnectionsAa: Vector potentiala: scalar potentialab: Vector spin connection0ab: Scalar spin connection

    Please observe the Einstein summation convention!

  • *ECE Field Equations in Terms of Potential I

  • *Antisymmetry Conditions ofECE Field Equations IElectric antisymmetry constraints:Magnetic antisymmetry constraints:Or simplifiedLindstrom constraint:

  • *Field-Potential Relations IIOne Polarization onlyPotentials and Spin ConnectionsA: Vector potential: scalar potential: Vector spin connection0: Scalar spin connection

  • *ECE Field Equations in Terms of Potential II

  • *Antisymmetry Conditions ofECE Field Equations IIAll these relations appear in addition to the ECE field equations and areconstraints of them. They replace Lorenz Gauge invariance and can be used to derive special properties.Electric antisymmetry constraints:Magnetic antisymmetry constraints:or:

  • *Relation between Potentials and Spin Connections derived from Antisymmetry Conditions

  • *Alternative I: ECE Field Equations with Alternative Current Definitions (a)*

  • *Alternative I: ECE Field Equations with Alternative Current Definitions (b)*

  • *Alternative II: ECE Field Equations with currents defined by curvature onlye0, Je0: normal charge density and currente1, Je1: cold charge density and current

  • *Field-Potential Relations IIILinearized EquationsPotentials and Spin ConnectionsA: Vector potential: scalar potentialE: Vector spin connection of electric fieldB: Vector spin connection of magnetic field

  • *ECE Field Equations in Terms of Potential III

  • *Electric antisymmetry constraints:Antisymmetry Conditions ofECE Field Equations IIIMagnetic antisymmetry constraints:Define additional vectorsE1, E2, B1, B2:

  • Geometrical Definition of Charges/Currents*With polarization:Without polarization:

  • Curvature Vectors*

  • Additional Field Equations due to Vanishing Homogeneous Current*With polarization:Without polarization:

  • Resonance Equation of Scalar Torsion Field*With polarization:Without polarization:Physical units:

  • *Properties of ECE EquationsThe ECE equations in potential representation define a well-defined equation system (8 equations with 8 unknows), can be reduced by antisymmetry conditions and additional constraintsThere is much more structure in ECE than in standard theory (Maxwell-Heaviside)There is no gauge freedom in ECE theoryIn potential representation, the Gauss and Faraday law do not make sense in standard theory (see red fields)Resonance structures (self-enforcing oscillations) are possible in Coulomb and Ampre-Maxwell law

  • *Examples of Vector Spin Connectiontoroidal coil: = constlinear coil: = 0Vector spin connection represents rotation of plane of A potential

  • *ECE Field Equations of DynamicsOnly Newtons Law is known in the standard model.

  • *ECE Field Equations of DynamicsAlternative Form with Alternative gravito-magnetic field:

    Only Newtons Law is known in the standard model.

  • *Fields, Currents and Constantsg: gravity acceleration, h: gravito-magnetic fieldm: mass densitymh: gravito-magn. mass densityJm: mass currentjmh: gravito-magn. mass current

    Fields and CurrentsConstantsG: Newtons gravitational constantc: vacuum speed of light, required for correct physical units

  • *Force EquationsF [N]ForceM [Nm]TorqueT [1/m]Torsiong, h [m/s2]Accelerationm [kg]Massv [m/s]Mass velocityE0=mc2 [J]Rest energy [1/s]Rotation axis vectorL [Nms]Angular momentumPhysical quantities and units

  • *Field-Potential RelationsPotentials and Spin ConnectionsQ=cq: Vector potential: Scalar potential: Vector spin connection0: Scalar spin connection

  • *Physical UnitsMass Density/CurrentGravito-magnetic Density/CurrentFieldsPotentialsSpin ConnectionsConstants

  • *Antisymmetry Conditions ofECE Field Equations of Dynamics

  • *Properties of ECE Equations of DynamicsFully analogous to electrodynamic caseOnly the Newton law is known in classical mechanicsGravito-magnetic law is known experimentally (ESA experiment)There are two acceleration fields g and h, but only g is known todayh is an angular momentum field and measured in m/s2 (units chosen the same as for g)Mechanical spin connection resonance is possible as in electromagnetic caseGravito-magnetic current occurs only in case of coupling between translational and rotational motion

  • *Examples of ECE DynamicsRealisation of gravito-magnetic field hby a rotating mass cylinder(Ampere-Maxwell law)Detection of h field by mechanical Lorentz force FLv: velocity of mass mhFLv

  • *Polarization and MagnetizationElectromagnetism

    P: PolarizationM: MagnetizationDynamics

    pm: mass polarizationmm: mass magnetizationNote: The definitions of pm and mm, compared to g and h, differ from the electrodynamic analogue concerning constants and units.

  • *Field Equations for Polarizable/Magnetizable MatterElectromagnetism

    D: electric displacementH: (pure) magnetic fieldDynamics

    g: mechanical displacementh0: (pure) gravito-magnetic field

  • *ECE Field Equations of Dynamicsin Momentum RepresentationNone of these Laws is known in the standard model.

  • *Physical UnitsMass Density/CurrentGravito-magnetic Density/CurrentFieldsFields and CurrentsL: orbital angular momentum S: spin angular momentump: linear momentumm: mass density mh: gravito-magn. mass densityJm: mass current jmh: gravito-magn. mass currentV: volume of space [m3] m: mass=integral of mass density