Question #42937

Two unequal point charges create a neutral equilibrium point at the origin ($x=0$). Near this point, the static electric field along the x-axis is approximately given by $\vec{E} = -k x \hat{i}$, where $k$ is a positive constant. A dust particle of initial mass $m_0$ and constant positive charge $q$ is projected from the origin along the positive x-axis with an initial velocity $v_0$. The region is filled with a uniform, stationary cloud of neutral dust. As the particle moves, it sweeps up and accretes this dust such that its mass increases at a constant rate with respect to distance, given by $\frac{dm}{dx} = b$ (where $b$ is a positive constant). Assuming no other forces act on the particle, what must be the value of $v_0$ so that the particle momentarily comes to rest exactly at $x = \frac{3m_0}{2b}$?