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, the equation was labeled by Selvan:
Equation
Rosser's Equation (Equation (19)) is given by the following:
-µ0J + µ0ε0∇∂ɸ/∂t = -µ0(J – ε0∇∂ɸ/∂t) = -µ0Jt
where:
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:
References
Rosser's equation (physics) Wikipedia(Text) CC BY-SA