The magnetic force on a moving charge is F_B = q v × B. What is the magnitude when v is perpendicular to B?

The magnetic force on a moving charge is F_B = q v × B. What is the magnitude when v is perpendicular to B?

• A. F = q v B
• B. F = q v B cos θ
• C. F = q v B sin θ
• D. F = 1/2 q v B

Answer: (A)

Magnetic force comes from the cross product, so its magnitude is |F| = q v B sin θ, where θ is the angle between the velocity v and the magnetic field B. If they are perpendicular, θ = 90°, and sin 90° = 1, giving |F| = q v B. The cos factor belongs to the dot product, not this cross product, and there’s no extra 1/2 factor in the magnetic force formula. The force points perpendicular to both v and B (right-hand rule).

Magnetic force comes from the cross product, so its magnitude is |F| = q v B sin θ, where θ is the angle between the velocity v and the magnetic field B. If they are perpendicular, θ = 90°, and sin 90° = 1, giving |F| = q v B. The cos factor belongs to the dot product, not this cross product, and there’s no extra 1/2 factor in the magnetic force formula. The force points perpendicular to both v and B (right-hand rule).