Given a system of $N$ charged point particles in $\mathbb{R}^3$ of the same charge which interact according to Coulomb law (thus they repell one from each other). Is it possible that the system remains in a fixed ball all the time?

More explicitly, denote $m_1,\dots, m_N>0$ the masses of the particles. Assume that the $i$ particle acts on $j$th one with the force

$$\vec F_{ij}=\frac{k_ee_ie_j}{|\vec x_j-\vec x_i|^3}\cdot (\vec x_j-\vec x_i), $$ where $k_e>0$ is a constant, $e_i$ is a charge of $i$th particle such that $e_ie_j>0$, $\vec x_i$ is the location of the $i$th particle. The equations of motions are $$m_i\frac{d^2 x_j}{dt^2}=\sum_{i\ne j}\vec F_{ij}, \mbox{ where } j=1,\dots,N.$$

The question is whether there is a solution such that for some $R$ one has $$||\vec x_i(t)||<R \mbox{ for all } t>0, \, i=1,\dots, N.$$