A weightless rod of a length $2R$ is placed perpendicular to a uniform magnetic field $\vec B$. Two identical small balls of mass $m$ and charge $q$ each are attached at the rod ends. Let us direct $z$-axis along the magnetic field and place the origin at the rod center. The balls are given the same initial velocity $v$ but in opposite directions so that one of the velocities is precisely in the $z$-direction. What are the maximum coordinates $z_\mathrm {max}$ of the balls? Express your answer in terms of $q, B, m, v$, and $R$. Find the magnitude of the ball accelerations at this moment and express your answer in terms of $q, B, m, v, R$, and $z_\mathrm{max}$.