Which equation gives the magnetic force on a moving charge?

• A. F = q v × B
• B. F = q E
• C. F = B v
• D. F = qB

Answer: (A)

Magnetic force on a moving charge comes from the cross product of the velocity and the magnetic field: F = q v × B. This means the force is perpendicular to both the particle’s motion and the magnetic field, with a magnitude given by F = q v B sin(theta), where theta is the angle between v and B. When the velocity is perpendicular to B, sin(theta) = 1 and the force is F = q v B, pointing in the direction given by the right-hand rule for a positive charge. The other forms miss the essential dependence on motion or the cross-product geometry: F = q E describes the electric force from an electric field, not the magnetic interaction; F = B v isn’t a valid force expression because it ignores the necessary cross product and proper units; F = q B lacks velocity altogether and isn’t dimensionally correct for a force in general.