Rosser's equation (physics)
This article is about the Rosser's equation in physics. For the similarly-named equation in economics, see Rosser's equation.
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]
| “ | It can thus be seen that Rosser's Equation (19) in terms of transverse current density has actually hidden away the displacement current. | ” |
Equation
Rosser's Equation (Equation (19)) is given by the following:
-µ0J + µ0ε0∇∂ɸ/∂t = -µ0(J – ε0∇∂ɸ/∂t) = -µ0Jt
where:
- is the conduction-current density,
- is the transverse current density,
- is time, and
- 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:
| “ | A lot of confusion about the role of the displacement current in empty space might be avoided, if it were called something else that did not include the term current. If a name is needed, it could be called the Maxwell term in honour of the man who first introduced it. | ” |
References
- ↑ 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.
- ↑ 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.
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