Question #42840

A solid non-conducting sphere of radius $R$ has a uniform volume charge density $\rho$. A spherical cavity of radius $r$ ($r < R$) is made inside the sphere. The center of the cavity is displaced from the center of the sphere by a constant vector $\vec{d}$. A particle of mass $m$ and charge $q$ is placed inside the cavity. The particle is attached to the center of the cavity by a light insulating spring of force constant $k$ and zero natural length. The entire sphere is then given a constant acceleration $\vec{a}$ in a direction perpendicular to $\vec{d}$. If the particle is released from rest relative to the cavity from the cavity's center, what is the maximum speed of the particle in the reference frame of the sphere? (Ignore gravity and assume the particle does not collide with the cavity walls).