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Potentials for a Cylindrical Electromagnetic Cavity
"... Deduce scalar and vector potentials relevant to the lowest electromagnetic mode in a right circular cylindrical cavity of radius R and axial extend 2D, assuming the walls to be perfect conductors, and the interior of the cavity to be vacuum. 2 Solution For the case of a rectangular cavity, see [1]. ..."
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Deduce scalar and vector potentials relevant to the lowest electromagnetic mode in a right circular cylindrical cavity of radius R and axial extend 2D, assuming the walls to be perfect conductors, and the interior of the cavity to be vacuum. 2 Solution For the case of a rectangular cavity, see [1]. 2.1 E and B Fields of the Cavity Modes In cylindrical coordinates (r, φ, z)withthezaxis being that of the cavity, only Ez and Bφ are nonzero, such that for time dependence e −iωt we have (in Gaussian units; see, for example, sec. 8.7 of [2]) where the resonant frequency is Ez = E0 J0(kr) e −iωt, (1) Bφ = −iE0 J1(kr) e −iωt, (2) ω = kc = 2.405c, (3) R such that J0(kR) = 0 so the tangential electric field is zero at r = R, andcis the speed of light in vacuum. The magnetic field is related to the electric field by Faraday’s law,
2.1 Electromagnetic Waves
, 1979
"... Discuss how the concept of gauge invariance can lead to an understanding of how/why electromagnetic waves can have only two independent polarization states. Comment also on gravitational waves. ..."
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Discuss how the concept of gauge invariance can lead to an understanding of how/why electromagnetic waves can have only two independent polarization states. Comment also on gravitational waves.