Circular Motion In A Magnetic Field

When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force provides the centripetal force needed for circular motion, as described in NCERT Class 12, Chapter 4 (Moving Charges and Magnetism). Setting the Lorentz force equal to the centripetal force: $qvB=\frac{m{v}^2}{r}$, which rearranges to $r=\frac{mv}{qB}$. This shows the radius is directly proportional to the speed when charge, mass, and field are constant. Therefore, doubling the speed doubles the radius, giving a new radius of $2r$. The option $r/2$ inverts the proportionality and is incorrect. The option $4r$ mistakenly treats radius as proportional to $v^2$, which would be true for kinetic energy but not for radius. The option $r$ ignores the dependence on speed entirely. Plausibility check: dimensionally $\frac{mv}{qB}$ gives $\frac{\text{kg}\cdot \text{m/s}}{\text{C}\cdot \text{T}}=\text{m}$, confirming a length, and a faster particle logically sweeps a wider circle since it resists being turned more strongly.