Question

A particle of mass m and charge q moves with speed v perpendicular to a magnetic field B. Equating the magnetic force to the centripetal force, the radius of the circular path is:

Options

• \[r = \frac{qB}{mv}\]

• \[r = \frac{mv}{qB}\]

• \[r = \frac{qvB}{m}\]

• \[r = \frac{mB}{qv}\]

Answer 1

The magnetic force F = qvB provides the centripetal force \[\frac{mv^2}{r}\]. Equating both: \[\frac{mv^2}{r} = qvB\]. Solving for the radius gives \[r = \frac{mv}{qB}\]. Larger momentum mv means a larger radius — heavier or faster particles trace wider circles.