A charged particle with charge q moves with velocity perpendicular to B. Which is the correct expression for the magnitude of the magnetic force on the particle?

A charged particle with charge q moves with velocity perpendicular to B. Which is the correct expression for the magnitude of the magnetic force on the particle?

• A. F = q v B
• B. F = q v B sin θ
• C. F = |q| v B
• D. F = |q| v B / c

Answer: (C)

The magnetic force on a moving charge comes from the cross product F = q v × B, so its magnitude is F = |q| v B sin θ, where θ is the angle between the velocity and the magnetic field. When the velocity is perpendicular to B, θ = 90°, and sin 90° = 1, giving F = |q| v B. The magnitude must be nonnegative, so the absolute value of the charge is used; if q is positive this matches q v B, but if q is negative the direction of the force reverses while the magnitude remains |q| v B. The other expressions either ignore the absolute value, include an extra c factor (not needed in SI), or use sin θ unnecessarily since the angle is already known to be 90 degrees.

The magnetic force on a moving charge comes from the cross product F = q v × B, so its magnitude is F = |q| v B sin θ, where θ is the angle between the velocity and the magnetic field. When the velocity is perpendicular to B, θ = 90°, and sin 90° = 1, giving F = |q| v B. The magnitude must be nonnegative, so the absolute value of the charge is used; if q is positive this matches q v B, but if q is negative the direction of the force reverses while the magnitude remains |q| v B. The other expressions either ignore the absolute value, include an extra c factor (not needed in SI), or use sin θ unnecessarily since the angle is already known to be 90 degrees.