Lorentz force
Summary
The Lorentz force is the total electromagnetic force on a charge q moving at velocity v through electric field E and magnetic field B. On the MCAT it usually means the magnetic part, F = qvB sinθ, which is perpendicular to v, so it bends the path without changing speed.
Detail
Meaning: A charge in an electric field feels qE whether or not it moves. A moving charge in a magnetic field also feels a magnetic force. The Lorentz force is the sum. The magnetic part is perpendicular to both v and B, so it changes direction but not speed, and does no work. If v is perpendicular to B, the path is a circle; with a component along B, it is a helix.
Equation: F = q(E + v × B). F is force (N), q charge (C), E electric field (N/C or V/m), v velocity (m/s), B magnetic field (T). The magnetic magnitude is qvB sinθ, with θ the angle between v and B. For circular motion, r = mv/(qB), with m in kg and r in m.
On the MCAT: Passages use mass spectrometers, cyclotrons and velocity selectors (qE = qvB, so v = E/B). Predict deflection with the right-hand rule and compare radii for different ions.
Common confusion: Students think the magnetic force can speed a charge up. It is perpendicular to v, so it does no work and kinetic energy stays constant. It is zero if v = 0 or v is parallel to B. For a negative charge, reverse the right-hand-rule direction.
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.