Lorentz-violating electrodynamics

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In physics, Rosser's equation aids in understanding the role of displacement current in Maxwell's equations, given that there is no ether in empty space as initially assumed by Maxwell. Due originally to William G.V. Rosser,[1] the equation was labeled by Selvan:[2]

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Equation

Rosser's Equation (Equation (19)) is given by the following:

-µ0J + µ0ε0∇∂ɸ/∂t = -µ0(J – ε0∇∂ɸ/∂t) = -µ0Jt

where:

J is the conduction-current density,
J,t is the transverse current density,
t is time, and
ϕ is the scalar potential.

To understand Selvan's quotation we need the following terms: ρ is charge density, A is vector potential, and D is displacement. Given these, the following hold:

ε0 = ρ/[∇(-∇ɸ - ∂A/∂t)]

µ0 = -∇2A/(J + ∂D/∂t)

The term ∂D/∂t is the displacement current that Selvan notes is "hidden away" in Rosser's Equation. Selvan (ibid.) quotes Rosser himself as follows:

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References

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  1. Rosser, W.G.V., 1976, December. "Does the Displacement Current in Empty Space Produce a Magnetic Field?" American Journal of Physics, vol. 44, no. 12, pp. 1221-1223.
  2. Selvan, T. Krishnasamy, 2009, June. "A Revisiting of Scientific and Philosophical Perspectives on Maxwell's Displacement Current," IEEE Antennas and Propagation Magazine, vol. 51, no. 3, pp. 36-46.