Talk:Lorentz force

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
 * $$\mathbf{F} = q\mathbf{E} + q\mathbf{v} \times \mathbf{B}$$

for an isolated particle, then in a material medium it should take the form
 * $$\mathbf{f} = \rho \mathbf{E} + \mathbf{J} \times \mathbf{B}$$

where: f is the density of force; &rho; 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
 * $$\rho = \rho_f - \nabla \cdot \mathbf P$$

where: &rho;f is the density of free charge; and P is the polarization density. And we also have
 * $$\mathbf{J} = \mathbf{J}_f + \nabla\times\mathbf{M} + \frac{\partial\mathbf{P}}{\partial t}$$

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

If we put these together, we get
 * $$\mathbf{f} = (\rho_f - \nabla \cdot \mathbf P) \mathbf{E} + (\mathbf{J}_f + \nabla\times\mathbf{M} + \frac{\partial\mathbf{P}}{\partial t}) \times \mathbf{B}$$.

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)