Physics

The key is recognizing that acceleration through a potential difference gives the electron kinetic energy, which determines how fast it moves, while the magnetic field's job is to curve that path into a circle. When you increase the voltage, the electron moves faster, so you need a stronger magnetic field to keep the same radius—the magnetic force must increase to match the higher momentum. Use energy conservation to find how velocity changes with voltage, then apply the circular motion condition $qvB = \frac{mv^2}{r}$ to see how $B$ must scale.

The key is recognizing that acceleration through a potential difference gives the electron kinetic energy, which determines how fast it moves, while the magnetic field's job is to curve that path into a circle. When you increase the voltage, the electron moves faster, so you need a stronger magnetic field to keep the same radius—the magnetic force must increase to match the higher momentum. Use energy conservation to find how velocity changes with voltage, then apply the circular motion condition $qvB = \frac{mv^2}{r}$ to see how $B$ must scale.