Question #43823

A long, thin, non-conducting cylindrical shell of radius $R$ rotates about its longitudinal axis with a constant angular velocity $\omega_0$. Initially ($t=0$), the shell has a uniform linear number density $N_0$ of radioactive isotope $A$ (charge $+q$). Isotope $A$ undergoes a successive decay chain: $A \to B \to C$, where the decay constant for $A \to B$ is $2\lambda$ and for $B \to C$ is $\lambda$. Isotope $B$ has charge $+2q$ and Isotope $C$ has charge $+4q$. All isotopes remain firmly attached to the rotating shell. A particle $P$ of mass $m$ and charge $+Q$ is constrained to move in a smooth, stationary, non-conducting circular tube of radius $r$ ($r < R$) coaxial with the cylinder. At $t=0$, particle $P$ is at rest. Find the speed of particle $P$ at the exact instant when the number of $B$ nuclei on the shell reaches its maximum value. (Assume the system is in a vacuum and ignore any magnetic field produced by particle $P$ itself).