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GED:010117Crossed E=3E0 x-hat and B=4E0 z-hat become a pure magnetic field after the boost v=-(3/4) y-hat

Ged Crossed Field InvariantsGed Boost TO Magnetic Frame

Covariant Maxwell theory, gauge structure, and differential formsGraduate Electrodynamics · Mixed review

GED:010118Residual gauge alpha=-1 on the null wave (k,eps)=((2,0,0,2),(2,3,4,2)) leaves transverse (0,3,4,0) of Minkowski norm -25

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Ged Null Plane Wave LorenzGed Residual Gauge Transverse

Covariant Maxwell theory, gauge structure, and differential formsGraduate Electrodynamics · Mixed review

GED:010130Born–Infeld point charge saturates E=b at the origin and Φ0=b r0 Γ(1/4)²/(4√π)

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Ged Born Infeld Constitutive InversionGed Born Infeld Origin Potential

Covariant Maxwell theory, gauge structure, and differential formsGraduate Electrodynamics · Mixed review

GED:010219The Yukawa Green function e^{-kappa r}/(4 pi r) has flux weight e^{-kappa r}(1+kappa r) -> 1 and L1 mass 1/kappa^2

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Ged Yukawa Green RadialGed Green Flux L1 Mass

Green functions, reciprocity, and boundary-value methodsGraduate Electrodynamics · Mixed review

GED:010227An isolated conducting disk stores sqrt(3)/2 of its charge in the outer half-radius rim.

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Ged Conducting Disk Both Face DensityGed Disk Rim Charge Fraction

Green functions, reciprocity, and boundary-value methodsGraduate Electrodynamics · Mixed review

GED:010320Two in-phase z-dipoles one wavelength apart radiate 2 sin(theta) cos(pi cos theta) with total power 2-3/(2 pi^2) times one dipole

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Ged Two Element Dipole ArrayGed Dipole Pair Power Integral

Multipole radiation and relativistic sourcesGraduate Electrodynamics · Mixed review

GED:010321A rotating magnetic dipole m=m0(cos omega t x-hat + sin omega t y-hat) has averaged factor (1+cos^2 theta)/2 and total twice a linear component

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Ged Rotating Magnetic DipoleGed Circular Dipole Pattern

Multipole radiation and relativistic sourcesGraduate Electrodynamics · Mixed review

GED:010331A charge stopping from v0 x-hat leaves radiation memory q v0 x-hat/(4πε0 c² R) on +z

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Ged Nonrelativistic Electric MemoryGed Radiation Memory Angular Integral

Multipole radiation and relativistic sourcesGraduate Electrodynamics · Mixed review

GED:010422A unit-line lossless iris with normalized shunt y=2i has r=-(1+i)/2, t=(1-i)/2, and S-eigenvalues -i and -1

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Ged Lossless Iris Shunt SmatrixGed Lossless Smatrix Eigenvalues

Waveguides, resonators, and electromagnetic scatteringGraduate Electrodynamics · Mixed review

GED:010423A dielectric sphere with εr=4 has Rayleigh polarizability 2π ε0 a³ and scattering efficiency (2/3)(ka)⁴

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Ged Rayleigh Dielectric PolarizabilityGed Rayleigh Scattering Efficiency

Waveguides, resonators, and electromagnetic scatteringGraduate Electrodynamics · Mixed review

GED:010428A single lossless p-wave with δ1=π/6 sits at a quarter of the 12π/k² unitarity ceiling

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Ged Lossless Single Pwave AmplitudeGed Optical Theorem Unitarity Ceiling

Waveguides, resonators, and electromagnetic scatteringGraduate Electrodynamics · Mixed review

GED:010524The Lorentz oscillator with ωp=ω0 and γ=ω0/2 has on-resonance susceptibility 2i and poles at (±√15-i)ω0/4

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Ged Lorentz ON Resonance SusceptibilityGed Lorentz Pole Half Plane

Dispersive media, response, and causalityGraduate Electrodynamics · Mixed review

GED:010525A monochromatic slab with εr=μr=-1 supports E=x̂, H=+ŷ, ⟨S⟩=+ẑ and phase toward -ẑ at matched Z=+Z0

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Ged Negative Index ImpedanceGed Backward Wave Poynting

Dispersive media, response, and causalityGraduate Electrodynamics · Mixed review

GED:010626Uniform-field hyperbolic motion from rest has γ=√(1+(t/τ)²) and proper time τ ln 2 at t=3τ/4

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Ged Uniform Field HyperbolaGed Hyperbola Proper Time

Charged-particle dynamics, self-fields, and radiation reactionGraduate Electrodynamics · Mixed review

GED:010629Penning modes at ωc=5Ω and ωz=2√2 Ω split as ω+=4Ω and ω−=Ω with product 4Ω²

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Ged Penning Radial DiscriminantGed Magnetron Modified Cyclotron Split

Charged-particle dynamics, self-fields, and radiation reactionGraduate Electrodynamics · Mixed review

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GED:010117Crossed E=3E0 x-hat and B=4E0 z-hat become a pure magnetic field after the boost v=-(3/4) y-hat

GED:010118Residual gauge alpha=-1 on the null wave (k,eps)=((2,0,0,2),(2,3,4,2)) leaves transverse (0,3,4,0) of Minkowski norm -25

GED:010130Born–Infeld point charge saturates E=b at the origin and Φ0=b r0 Γ(1/4)²/(4√π)

GED:010219The Yukawa Green function e^{-kappa r}/(4 pi r) has flux weight e^{-kappa r}(1+kappa r) -> 1 and L1 mass 1/kappa^2

GED:010227An isolated conducting disk stores sqrt(3)/2 of its charge in the outer half-radius rim.

GED:010320Two in-phase z-dipoles one wavelength apart radiate 2 sin(theta) cos(pi cos theta) with total power 2-3/(2 pi^2) times one dipole

GED:010321A rotating magnetic dipole m=m0(cos omega t x-hat + sin omega t y-hat) has averaged factor (1+cos^2 theta)/2 and total twice a linear component

GED:010331A charge stopping from v0 x-hat leaves radiation memory q v0 x-hat/(4πε0 c² R) on +z

GED:010422A unit-line lossless iris with normalized shunt y=2i has r=-(1+i)/2, t=(1-i)/2, and S-eigenvalues -i and -1

GED:010423A dielectric sphere with εr=4 has Rayleigh polarizability 2π ε0 a³ and scattering efficiency (2/3)(ka)⁴

GED:010428A single lossless p-wave with δ1=π/6 sits at a quarter of the 12π/k² unitarity ceiling

GED:010524The Lorentz oscillator with ωp=ω0 and γ=ω0/2 has on-resonance susceptibility 2i and poles at (±√15-i)ω0/4

GED:010525A monochromatic slab with εr=μr=-1 supports E=x̂, H=+ŷ, ⟨S⟩=+ẑ and phase toward -ẑ at matched Z=+Z0

GED:010626Uniform-field hyperbolic motion from rest has γ=√(1+(t/τ)²) and proper time τ ln 2 at t=3τ/4

GED:010629Penning modes at ωc=5Ω and ωz=2√2 Ω split as ω+=4Ω and ω−=Ω with product 4Ω²

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GED:010117Crossed E=3E0 x-hat and B=4E0 z-hat become a pure magnetic field after the boost v=-(3/4) y-hat

GED:010118Residual gauge alpha=-1 on the null wave (k,eps)=((2,0,0,2),(2,3,4,2)) leaves transverse (0,3,4,0) of Minkowski norm -25

GED:010130Born–Infeld point charge saturates E=b at the origin and Φ0=b r0 Γ(1/4)²/(4√π)

GED:010219The Yukawa Green function e^{-kappa r}/(4 pi r) has flux weight e^{-kappa r}(1+kappa r) -> 1 and L1 mass 1/kappa^2

GED:010227An isolated conducting disk stores sqrt(3)/2 of its charge in the outer half-radius rim.

GED:010320Two in-phase z-dipoles one wavelength apart radiate 2 sin(theta) cos(pi cos theta) with total power 2-3/(2 pi^2) times one dipole

GED:010321A rotating magnetic dipole m=m0(cos omega t x-hat + sin omega t y-hat) has averaged factor (1+cos^2 theta)/2 and total twice a linear component

GED:010331A charge stopping from v0 x-hat leaves radiation memory q v0 x-hat/(4πε0 c² R) on +z

GED:010422A unit-line lossless iris with normalized shunt y=2i has r=-(1+i)/2, t=(1-i)/2, and S-eigenvalues -i and -1

GED:010423A dielectric sphere with εr=4 has Rayleigh polarizability 2π ε0 a³ and scattering efficiency (2/3)(ka)⁴

GED:010428A single lossless p-wave with δ1=π/6 sits at a quarter of the 12π/k² unitarity ceiling

GED:010524The Lorentz oscillator with ωp=ω0 and γ=ω0/2 has on-resonance susceptibility 2i and poles at (±√15-i)ω0/4

GED:010525A monochromatic slab with εr=μr=-1 supports E=x̂, H=+ŷ, ⟨S⟩=+ẑ and phase toward -ẑ at matched Z=+Z0

GED:010626Uniform-field hyperbolic motion from rest has γ=√(1+(t/τ)²) and proper time τ ln 2 at t=3τ/4

GED:010629Penning modes at ωc=5Ω and ωz=2√2 Ω split as ω+=4Ω and ω−=Ω with product 4Ω²

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Problem results

GED:010117Crossed E=3E0 x-hat and B=4E0 z-hat become a pure magnetic field after the boost v=-(3/4) y-hatView problem statement

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Problem results

GED:010117Crossed E=3E0 x-hat and B=4E0 z-hat become a pure magnetic field after the boost v=-(3/4) y-hatView problem statement

GED:010117Crossed E=3E0 x-hat and B=4E0 z-hat become a pure magnetic field after the boost v=-(3/4) y-hat

GED:010117Crossed E=3E0 x-hat and B=4E0 z-hat become a pure magnetic field after the boost v=-(3/4) y-hat