Question #43009

A solid conducting sphere of radius $R$ and total charge $Q > 0$ is rigidly fixed at the origin of a reference frame attached to a spacecraft. The spacecraft is accelerating in deep space with a constant acceleration $\vec{a} = \frac{qQ}{16\pi\epsilon_0 m R^2} \hat{i}$, where $\epsilon_0$ is the vacuum permittivity. A small particle of mass $m$ and charge $q > 0$ is projected from the position $x = 3R$ on the x-axis towards the origin, with an initial speed $v_0$ relative to the spacecraft. Assume the charge $Q$ remains uniformly distributed on the sphere. What is the minimum value of $v_0$ required for the particle to strike the surface of the sphere?