formulas:lorentz_force_law
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formulas:lorentz_force_law [2018/04/14 10:26] aresmarrero [Concrete] |
formulas:lorentz_force_law [2018/05/13 09:18] (current) jakobadmin ↷ Page moved from equations:lorentz_force_law to formulas:lorentz_force_law |
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| <tabbox Concrete> | <tabbox Concrete> | ||
| - | ---- | ||
| - | |||
| **Derivation** | **Derivation** | ||
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| &= e\left(\frac{\partial A_j}{\partial q^i} - \frac{\partial A_i}{\partial q^j}\right)\dot{q}^j . | &= e\left(\frac{\partial A_j}{\partial q^i} - \frac{\partial A_i}{\partial q^j}\right)\dot{q}^j . | ||
| \end{align*} | \end{align*} | ||
| - | Here, term in parentheses is $\fvect{F}_{ij}=$ the electromagnetic field, $F=dA$. Therefore, the equations of motion are | + | Here, term in parentheses is $F_{ij}=$ the electromagnetic field, $F=dA$. Therefore, the equations of motion are |
| \begin{equation} | \begin{equation} | ||
| - | \boxed{ | + | m\frac{d v_i}{dt} = e F_{ij}\dot{q}^j, |
| - | \eqngapabove \gapleft | + | |
| - | m\frac{d v_i}{dt} = e\fvect{F}_{ij}\dot{q}^j, \quad\text{(Lorentz force law)} | + | |
| - | \gapright \eqngapbelow | + | |
| - | } | + | |
| \end{equation} | \end{equation} | ||
| - | which we call the Lorentz law.) | + | which we call the Lorentz law. |
| <tabbox Abstract> | <tabbox Abstract> | ||
formulas/lorentz_force_law.1523694369.txt.gz · Last modified: 2018/04/14 08:26 (external edit)
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