Solution
= Solution
The equation is $m\ddot x=-\nabla V+q\dot x\times B$; the magnetic force does no work. For $B=\beta\hat r/r^2$, the triple-product identity gives $\dot L=q\beta\,d\hat r/dt$, so $J=L-q\beta\hat r$ is conserved. Since $J\cdot\hat r=-q\beta$, the trajectory lies on a cone with $\cos\alpha=-q\beta/|J|$.