Magnetism and Moving Charges

A magnetic force acts perpendicular to the velocity at every instant, so it does zero work and cannot change a particle's speed: it steers only. With constant speed and a constant-magnitude perpendicular force, the perpendicular motion is a circle of radius $r = mv_\perp/(|q|B)$, and any velocity along the field survives untouched, making the general path a helix. Dividing the circumference by the speed cancels the speed entirely, leaving the period $T = 2\pi m/(|q|B)$, which is the reason a fixed-frequency cyclotron stays in step with a particle whose orbit keeps growing. In crossed fields, the speed-independent electric force balances the speed-dependent magnetic one at exactly $v = E/B$.

Four errors dominate. Running the right-hand rule on an electron and reporting the answer without the single sign flip, or flipping twice by also reversing the velocity for electron flow. Letting the magnetic field add or drain kinetic energy, when $(\vec{v}\times\vec{B})\cdot\vec{v} = 0$ forbids it. Shrinking the radius for a faster particle, or shortening its period, when $r$ scales with $v$ and $T$ does not depend on $v$ at all. And treating a velocity selector as a universal null, when only $v = E/B$ passes and a faster particle bends toward the magnetic force.