Question #42931

A particle of mass $m$ and charge $-q$ ($q > 0$) is projected inside a fixed non-conducting solid sphere of radius $R$ having a uniform volume charge density $\rho$ ($\rho > 0$). The particle experiences a velocity-dependent drag force $\vec{F}_d = -b\vec{v}$, where $b$ is a positive constant and $\vec{v}$ is its instantaneous velocity. The particle is projected such that it follows a spiraling trajectory where the angle between its velocity vector and its radial position vector (measured from the center of the sphere) remains constant over time. Assuming the particle remains inside the sphere, what is the ratio of the magnitude of its tangential velocity component to the magnitude of its radial velocity component during this motion? ($\epsilon_0$ is the permittivity of free space)