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Talk:Lorentz force

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Presumably temporary problems

   I'm about to revert myself, and work out my confusion before next saving another revision, that should actually be better than what i found. (I'm about 50 years rusty on this, and i'd better sharing my misgivings about what i found, later in this section, before saving the fix that had seemed just around the corner.)
--Jerzy•t 05:58, 8 October 2017 (UTC)

Polarization and magnetization

If the Lorentz force takes the form

F = q E + q v × B {\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} }

for an isolated particle, then in a material medium it should take the form

f = ρ E + J × B {\displaystyle \mathbf {f} =\rho \mathbf {E} +\mathbf {J} \times \mathbf {B} }

where: f is the density of force; ρ is the density of total charge; and J is the density of total current. What if we then separate the total charge and current into their free and bound parts?

From the article on Polarization density, we have

ρ = ρ f − ∇ ⋅ P {\displaystyle \rho =\rho _{f}-\nabla \cdot \mathbf {P} }

where: ρf is the density of free charge; and P is the polarization density. And we also have

J = J f + ∇ × M + ∂ P ∂ t {\displaystyle \mathbf {J} =\mathbf {J} _{f}+\nabla \times \mathbf {M} +{\frac {\partial \mathbf {P} }{\partial t}}}

where: Jf is the density of free current; and M is the density of magnetization.

If we put these together, we get

f = ( ρ f − ∇ ⋅ P ) E + ( J f + ∇ × M + ∂ P ∂ t ) × B {\displaystyle \mathbf {f} =(\rho _{f}-\nabla \cdot \mathbf {P} )\mathbf {E} +(\mathbf {J} _{f}+\nabla \times \mathbf {M} +{\frac {\partial \mathbf {P} }{\partial t}})\times \mathbf {B} } .

Should this not be in the article? JRSpriggs (talk) 21:02, 19 October 2017 (UTC)

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Force on a current-carrying wire - SeVeN uP rule

A mnemonic for remembering the direction of the force resulting from ev x B is Seven Up. Imagine yourself on the particle going through the magnetic field forwards into the screen, that is the direction of 'V'. If the direction of B is 'S'outh <--- 'N'orth (i.e. right to left - magnetic field lines point north to south), the force is uP for a Positive particle (the same as for a conventional current) and dowN for a Negative particle. This spells out SVN (seven) and uP/dowN. The v in the middle represents the fact that the particle is moving through the magnetic field (S<-N). I think this is more memorable than all the rules with hands (right or left? which finger for which thing?) Acorrector (talk) 17:07, 3 May 2020 (UTC)

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