A magnetic field acts along the positive y-direction and a positively charged particle is moving along the positive x-direction. In which direction is the Lorentz force on the particle?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Positive z-direction
The magnetic part of the Lorentz force is \( \vec{F}=q\,(\vec{v}\times\vec{B}) \). It acts perpendicular to both the velocity and the magnetic field. The right-hand rule for the vector product gives its direction. The force reverses for a negative charge.
Option (1) Positive x-direction — Incorrect. The x-direction is the direction of the velocity, and the magnetic force is always perpendicular to the velocity.
Option (2) Negative z-direction — Incorrect. This is the direction of the force on a negative charge such as an electron. For a positive charge, the force is along \( \vec{v}\times\vec{B} \), which points the other way.
Option (3) Positive z-direction — Correct. With \( \vec{v} \) along \( \hat{\imath} \) and \( \vec{B} \) along \( \hat{\jmath} \), \( \vec{v}\times\vec{B} \) is along \( \hat{\imath}\times\hat{\jmath}=\hat{k} \), and for \( q\gt0 \) the force is along +z.
Option (4) The Lorentz force will be zero. — Incorrect. The force is zero only when \( \vec{v} \) is parallel or antiparallel to \( \vec{B} \). Here they are perpendicular, so the force has its largest value \( qvB \).
NCERT (2026-27):
Example 4.2
