What is the Lorentz force on a charge q moving with velocity v in electric field E and magnetic field B?

What is the Lorentz force on a charge q moving with velocity v in electric field E and magnetic field B?

• A. F = q( E + v × B )
• B. F = q( E − v × B )
• C. F = q( E + B × v )
• D. F = m a

Answer: (A)

The Lorentz force describes how a charged particle experiences force from electric and magnetic fields. The electric part acts along the field with magnitude qE, and the magnetic part depends on the velocity and the magnetic field. The magnetic force is given by q(v × B): it is perpendicular to both the velocity and the magnetic field, with magnitude q v B sinθ, where θ is the angle between v and B. When you combine them, the total force is F = q(E + v × B). This is why the correct form includes the plus sign and the cross product v × B. If the magnetic term used B × v instead of v × B, you’d get the opposite direction for the magnetic force because B × v = - (v × B). If you wrote E − v × B, that would flip the magnetic contribution, which is also incorrect. And F = m a is too general here: in fields, the acceleration is a = F/m = (q/m)(E + v × B), so you can’t express the force simply as m a without accounting for the qE and q(v × B) terms.

The Lorentz force describes how a charged particle experiences force from electric and magnetic fields. The electric part acts along the field with magnitude qE, and the magnetic part depends on the velocity and the magnetic field. The magnetic force is given by q(v × B): it is perpendicular to both the velocity and the magnetic field, with magnitude q v B sinθ, where θ is the angle between v and B. When you combine them, the total force is F = q(E + v × B). This is why the correct form includes the plus sign and the cross product v × B.

If the magnetic term used B × v instead of v × B, you’d get the opposite direction for the magnetic force because B × v = - (v × B). If you wrote E − v × B, that would flip the magnetic contribution, which is also incorrect. And F = m a is too general here: in fields, the acceleration is a = F/m = (q/m)(E + v × B), so you can’t express the force simply as m a without accounting for the qE and q(v × B) terms.