Physics

A charged particle in a magnetic field experiences a perpendicular force that curves its path into a circle—the magnetic force provides exactly the centripetal force needed. The key insight is to equate $qvB$ (magnetic force) with $\frac{mv^2}{r}$ (centripetal force requirement), solve for $v$, then substitute into the kinetic energy formula $K = \frac{1}{2}mv^2$. This lets you express $K$ purely in terms of the given quantities without needing to know the velocity explicitly.

A charged particle in a magnetic field experiences a perpendicular force that curves its path into a circle—the magnetic force provides exactly the centripetal force needed. The key insight is to equate $qvB$ (magnetic force) with $\frac{mv^2}{r}$ (centripetal force requirement), solve for $v$, then substitute into the kinetic energy formula $K = \frac{1}{2}mv^2$. This lets you express $K$ purely in terms of the given quantities without needing to know the velocity explicitly.