What is the magnitude of the magnetic force on a moving charge given by?

• A. F = q E
• B. F = μ0 I^2 L / (2π r)
• C. F = B I L
• D. F = q v B sin theta

Answer: (D)

The magnetic force on a moving charge comes from the Lorentz force, F = q v × B. Its magnitude is F = q v B sin theta, where theta is the angle between the velocity v and the magnetic field B. This tells you that the force depends on the charge, how fast it’s moving, the strength of the field, and how their directions relate. If v is perpendicular to B, sin theta = 1 and you get the largest force; if v is parallel to B, sin theta = 0 and the magnetic force vanishes. The direction is perpendicular to both v and B (use the right-hand rule for a positive charge, opposite for a negative charge).

The other expressions refer to different situations: F = qE is the electric force from an electric field, not a magnetic effect. F = μ0 I^2 L /(2π r) isn’t the standard result for the force on a single moving charge. F = B I L is the magnetic force on a current-carrying wire, given by F = I L × B, which involves many charges moving together, not a single moving charge.