- #1
ManDay
- 159
- 1
Is "E" in Maxwell-Equations really "E"?
Consider a perfectly static and spatially bound magnetic field B ∈ ℝ³ such that
B ≠ 0 ; ∂/∂t B = 0
further, a continuous, time-stationary, and spatially bound current j ∈ ℝ³ through that magnetic field
j ≠ 0 ; ∂/∂t j = 0 ; ∇ j = 0
which contributes to B but does not violate ∂/∂t B = 0. The initial charge distribution ρ = 0 for all space. It will therefore remain 0 for all times.
The Lorentz force predicts a force acting on a moving density of charge ρ'. j may be considered such a moving density superimposed by a stationary density -ρ' to satisfy ρ = 0. Therefore, the Lorentz force predicts an (effective) electric field, which is defined by its action on charges - but only on the moving ones, this time! Maxwell Equations, however, say that there is no electric field at all - on moving charges or stationary alike.
How can this be reconciled?
Consider a perfectly static and spatially bound magnetic field B ∈ ℝ³ such that
B ≠ 0 ; ∂/∂t B = 0
further, a continuous, time-stationary, and spatially bound current j ∈ ℝ³ through that magnetic field
j ≠ 0 ; ∂/∂t j = 0 ; ∇ j = 0
which contributes to B but does not violate ∂/∂t B = 0. The initial charge distribution ρ = 0 for all space. It will therefore remain 0 for all times.
The Lorentz force predicts a force acting on a moving density of charge ρ'. j may be considered such a moving density superimposed by a stationary density -ρ' to satisfy ρ = 0. Therefore, the Lorentz force predicts an (effective) electric field, which is defined by its action on charges - but only on the moving ones, this time! Maxwell Equations, however, say that there is no electric field at all - on moving charges or stationary alike.
How can this be reconciled?