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

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

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

Answer: (D)

The main idea is the Lorentz force law, which says a moving charge experiences a force that is the sum of an electric part and a magnetic part: F = q(E + v × B). The electric part qE acts along the electric field, while the magnetic part q(v × B) depends on the velocity and the magnetic field and is perpendicular to both v and B; its magnitude is q v B sinθ and its direction is given by the right-hand rule for a positive charge (reversing for negative q). Thus the total force is the vector q multiplied by the sum of E and v × B. This form is correct because it includes q multiplying both contributions and uses the correct cross product v × B for the magnetic part. Using B × v would give the opposite direction, and omitting q or misplacing it changes the magnitude and direction, so those forms don’t match the true Lorentz force.

The main idea is the Lorentz force law, which says a moving charge experiences a force that is the sum of an electric part and a magnetic part: F = q(E + v × B). The electric part qE acts along the electric field, while the magnetic part q(v × B) depends on the velocity and the magnetic field and is perpendicular to both v and B; its magnitude is q v B sinθ and its direction is given by the right-hand rule for a positive charge (reversing for negative q). Thus the total force is the vector q multiplied by the sum of E and v × B.

This form is correct because it includes q multiplying both contributions and uses the correct cross product v × B for the magnetic part. Using B × v would give the opposite direction, and omitting q or misplacing it changes the magnitude and direction, so those forms don’t match the true Lorentz force.