NDA (I) 2023 General Ability Test · Question 89 of 149

Correct — D, no deflecting force. The magnetic force on a moving charge is F = qv × B, with magnitude F = qvB·sinθ, where θ is the angle between the velocity and the field. Here the charge moves south while the field points north, so v and B are antiparallel and θ = 180°. Since sin 180° = 0, the force is zero — a charge moving parallel or antiparallel to the field feels no magnetic force, regardless of its sign.

• (a)a deflecting force towards north direction. — A magnetic force is always perpendicular to both v and B (from the cross product); it can never point along the field. Moreover, with v antiparallel to B the force is zero, so no north deflection occurs.
• (b)a deflecting force towards east direction. — A sideways (east) force would need a velocity component perpendicular to B, but here v is exactly antiparallel to B, giving sinθ = 0 and zero force.
• (c)a deflecting force towards west direction. — Same reason as the east option — there is no perpendicular component of velocity, so v × B = 0 and there is no westward (or any) deflection.

A charged particle moving through a magnetic field feels the Lorentz magnetic force F = qv × B. Its magnitude depends on the sine of the angle between velocity and field: it is greatest when the motion is perpendicular to the field (θ = 90°) and zero when the motion is along the field, either parallel (θ = 0°) or antiparallel (θ = 180°). The force, when it exists, is always perpendicular to both v and B.

The compass directions are a distraction. Once you see that 'south' and 'north' make v and B antiparallel, the sinθ factor collapses to zero and no force acts. Only a velocity component across the field lines would produce a deflection.

• Magnetic force on a moving charge: F = qv × B, magnitude qvB·sinθ.
• θ = 0° or 180° (motion along the field) gives sinθ = 0 and hence zero force.
• The force is maximum when v is perpendicular to B (θ = 90°).
• Any magnetic force is perpendicular to both the velocity and the field, so it never points along B.

• Trying to assign a compass direction to the force instead of first checking whether any force exists.
• Forgetting that motion parallel or antiparallel to the field yields zero magnetic force.

Asked as a conceptual electromagnetism item testing the sinθ dependence of the magnetic force.

No directly related past PYQ was found.

• practice — not a real PYQ

  A charged particle moving parallel to a uniform magnetic field experiences a magnetic force that is:

  • (a)maximum
  • (b)half the maximum
  • (c)zero
  • (d)directed along the field

  Answer(c) zero — because sinθ = 0 when v is along B.

• practice — not a real PYQ

  The magnetic force on a moving charge is maximum when the angle between its velocity and the magnetic field is:

  • (a)0°
  • (b)45°
  • (c)90°
  • (d)180°

  Answer(c) 90° — force magnitude is qvB·sinθ, maximum at θ = 90°.