A small magnetic needle is placed at a point P. It sets itself along the tangent to the magnetic field line through P. A charged particle now passes through P, moving at an angle to this field line. The magnetic force on the particle at P is directed
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → perpendicular to the field line at P
The needle shows the direction of \( \mathbf{B} \) at P. This direction is along the tangent to the field line. The force on a moving charge is \( \mathbf{F}=q\,\mathbf{v}\times\mathbf{B} \). A cross product is at right angles to both vectors in it. So the magnetic force is always normal to \( \mathbf{B} \).
Option (1) along the tangent to the field line at P — Incorrect. The tangent gives the direction of \( \mathbf{B} \). The force is at right angles to \( \mathbf{B} \), so it cannot act along the tangent. For this reason a magnetic field line is not a line of force.
Option (2) perpendicular to the field line at P — Correct. The force \( q\,\mathbf{v}\times\mathbf{B} \) is normal to \( \mathbf{B} \) at P. It is also normal to the velocity of the particle.
Option (3) along the velocity of the particle — Incorrect. The force is perpendicular to \( \mathbf{v} \). It changes the direction of motion. It does not push the particle along its path.
Option (4) nowhere, because the force is zero when the field does no work — Incorrect. The field does no work because the force is perpendicular to the velocity. The force itself is not zero. The particle moves at an angle \( \theta \) to \( \mathbf{B} \), so \( F=qvB\sin\theta \) is not zero.
NCERT (2026-27):
Example 5.4 – “(a) No. The magnetic force is always normal to B (remember magnetic force = qv × B). It is misleading to call magnetic field lines as lines of force.”