charge's velocity
Summary
A charge's velocity is the vector v (speed and direction) of a moving charge. It matters because a magnetic field exerts a force F = qvB sinθ only on a moving charge, perpendicular to v, so it changes the charge's direction but not its speed.
Detail
Meaning: Velocity is a vector, so direction matters as well as speed. A magnetic field acts only on the component of v perpendicular to B: a charge at rest, or moving parallel or antiparallel to B, feels no magnetic force. The force is perpendicular to both v and B, so it does no work and the speed stays constant. With v perpendicular to B the path is a circle; at other angles it is a helix.
Equation: F = qvB sinθ, where F is the magnetic force (N), q is the charge (C), v is the speed (m/s), B is the magnetic field (T), and θ is the angle between v and B. Circular path: r = mv/(qB), where m is mass (kg) and r is radius (m).
On the MCAT: Expect right-hand-rule direction questions (reverse the direction for a negative charge), radius comparisons for particles in a mass spectrometer, and velocity selectors where qE = qvB gives v = E/B for undeflected motion. Doubling v doubles both F and r.
Common confusion: A force does not mean the charge speeds up. The magnetic force is perpendicular to v, so it changes direction only and kinetic energy is unchanged. An electric field, by contrast, can change the speed.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.