Which factors determine the magnitude of the magnetic force on a moving charge?

• A. The velocity and the magnetic field only.
• B. The charge and velocity only.
• C. The magnetic field and velocity only.
• D. The charge, velocity, magnetic field, and angle.

Answer: (D)

The magnetic force on a moving charge follows F = q v × B, so its magnitude is F = |q| v B sin(theta), where theta is the angle between the velocity and the magnetic field. This shows four factors matter: the charge q, the speed v, the magnetic field strength B, and the angle between v and B. If any of these is zero, the force is zero. When theta is 0 or 180 degrees, the velocity runs parallel to the field and the force vanishes; when theta is 90 degrees, the force is at its maximum for those v and B. The perpendicular component of velocity, v_perp = v sin(theta), is what actually produces the force, so F = q B v_perp. Therefore, all four factors are needed to determine the magnitude.