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formulas:lorentz_force_law [2018/04/14 10:26] aresmarrero [Concrete] |
formulas:lorentz_force_law [2018/04/14 10:26] aresmarrero [Concrete] |
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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{ | \boxed{ | ||
- | \eqngapabove \gapleft | + | m\frac{d v_i}{dt} = e F_{ij}\dot{q}^j,} |
- | m\frac{d v_i}{dt} = e\fvect{F}_{ij}\dot{q}^j, \quad\text{(Lorentz force law)} | + | |
- | \gapright \eqngapbelow | + | |
} | } | ||
\end{equation} | \end{equation} |