I have just started to work on magnetic curves lying on magnetic field. I want to understand some more physical results. However, I am in need of your help to earn some perceptive to get me channelized to right path. I know that for any moving charged particle there is magnetic force on it induced from Lorentz force known as $F=q(v$x$M)$, where $q$ is the charge $v$ is the velocity vector and $M$ is the magnetic field. Since we also have $F=ma$ and in geometrical approach using Frenet frame on the moving particle we get $mk$N$=q(v$x$M)$, where $m$ is the mass, $k$ is the curvature of the curve and $N$ is the normal of the curve. Here, if we assume that $M=kB$, then we get $mk$N$=q(v$x$kB)$, by using ortogonality of the Frenet vector we finally obtain $mk$N$=kq(-$N$)$. Thus we get ratio of charge to mass -1. And my first questions are: Is that possible? What is the physical meaning of negative ratio? Where can I find extra useful information about this equality or mass-charge relation of the particle including physical consequences except for Wikipedia?
Thanks.