The movement of charges is based on Newton's second law and Coulomb's law of electrostatics.
The resultant force on charge $q_i$ is given by
$$
\vec{F}_i = \dfrac{1}{4\pi\epsilon_0}\sum_{j \neq i}^N \dfrac{q_iq_j}{r_{ij}^2}\hat{r}_{ij },
$$
where
- $N$: number of free charges
- $\epsilon_0$: electrostatic vacuum constant
The movement of the charges is damped by a force proportional to the speed:
$$
\vec{F}_\gamma = -\gamma \vec{v}
$$
The ODE system is solved by the fourth order Runge-Kutta method.
Other considerations:
- The values of $q$, $\gamma$ and the mass of the charges are given in arbitrary units.
- Collisions of charges with the boundary of the conductor are partially elastic.
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