- #1
Peeter
- 305
- 3
Basic electrostatics (as I've seen it presented) usually starts off with an implicit [itex]\mathbf{F} = q q_2 \hat{\mathbf{r}}/r^2 = q \mathbf{E}[/itex] definition of the electric field. Then with a limiting volume argument, you can then show that this can be expressed [itex]div \mathbf{E} = \rho[/itex]. Eventually one builds up to a complete picture where you have all the maxwell's equations together describing the true picture.
Now, you take the [itex]\mathbf{F} = q \mathbf{E}[/itex] that's correct for electrostatic, and lorentz transform appropriately sure enough you get the Lorentz force law.
From Maxwell's equations, assuming one is sufficiently talented mathematically, once given any particular charge and current distribution, you get these six position and time dependent numbers that are associated with that distribution. Now, is that really enough to describe the dynamics? Do you need this something extra like that statics [itex]\mathbf{F} = q \mathbf{E}[/itex] condition, or the [itex]-q \phi + \mathbf{v} \cdot \mathbf{B}[/itex] Lagrangian term to connect this to the dynamics?
I'm just trying to identify for myself the root laws that I'm working from while studying E&M. Would I be able to start with the 4 vector equations of maxwell and deduce everything else (if so that isn't obvious to me how to do so).
Now, you take the [itex]\mathbf{F} = q \mathbf{E}[/itex] that's correct for electrostatic, and lorentz transform appropriately sure enough you get the Lorentz force law.
From Maxwell's equations, assuming one is sufficiently talented mathematically, once given any particular charge and current distribution, you get these six position and time dependent numbers that are associated with that distribution. Now, is that really enough to describe the dynamics? Do you need this something extra like that statics [itex]\mathbf{F} = q \mathbf{E}[/itex] condition, or the [itex]-q \phi + \mathbf{v} \cdot \mathbf{B}[/itex] Lagrangian term to connect this to the dynamics?
I'm just trying to identify for myself the root laws that I'm working from while studying E&M. Would I be able to start with the 4 vector equations of maxwell and deduce everything else (if so that isn't obvious to me how to do so).