Which equation correctly expresses magnetic force on a moving charge in a magnetic field?

Which equation correctly expresses magnetic force on a moving charge in a magnetic field?

• A. F = ma
• B. Fb = qvB
• C. F = qE
• D. F = IV

Answer: (B)

Magnetic force on a moving charge depends on the charge, its speed, and the magnetic field, and it acts perpendicular to both the velocity and the field. The full expression uses a cross product: F = q v × B, with magnitude F = q v B sin(θ), where θ is the angle between the velocity and the magnetic field. When the velocity is perpendicular to the field (θ = 90°), sin(θ) = 1, so the magnitude simplifies to F = q v B. That’s why this form is the correct expression in that situation. The other options describe unrelated forces: Newton’s second law relates force to acceleration, the electric force is F = qE, and IV is a relation for electrical power, not force.

Magnetic force on a moving charge depends on the charge, its speed, and the magnetic field, and it acts perpendicular to both the velocity and the field. The full expression uses a cross product: F = q v × B, with magnitude F = q v B sin(θ), where θ is the angle between the velocity and the magnetic field. When the velocity is perpendicular to the field (θ = 90°), sin(θ) = 1, so the magnitude simplifies to F = q v B. That’s why this form is the correct expression in that situation. The other options describe unrelated forces: Newton’s second law relates force to acceleration, the electric force is F = qE, and IV is a relation for electrical power, not force.