A positive charge and a negative charge of the same magnitude enter a uniform magnetic field with equal velocities perpendicular to the field. Which of them experiences a force of greater magnitude?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both experience forces of equal magnitude
The magnetic force on a charge is \( \vec{F}=q\,\vec{v}\times\vec{B} \). When \( \vec{v} \) is perpendicular to \( \vec{B} \), its magnitude is \( |q|vB \). The sign of the charge decides only the direction of the force.
Option (1) The positive charge — Incorrect. The magnitude \( |q|vB \) depends on the size of the charge. Its sign does not change the magnitude, and both charges have the same size.
Option (2) The negative charge — Incorrect. A negative sign only reverses the direction of \( q\,\vec{v}\times\vec{B} \). It does not make the force larger.
Option (3) Both experience forces of equal magnitude — Correct. Both charges have the same \( |q| \), the same speed \( v \) and the same field \( B \), so both forces have the same magnitude \( |q|vB \). The forces are in opposite directions, so the two charges curve opposite ways.
Option (4) Cannot be predicted — Incorrect. The magnitude depends on \( |q| \), \( v \), \( B \) and the right angle between \( \vec{v} \) and \( \vec{B} \). All of these are the same for both charges, so the comparison is definite.
NCERT (2026-27):
Magnetic Field, Lorentz Force – “… Force on a negative charge is opposite to that on a positive charge.”
Motion in a Magnetic Field – “… If the velocity v is perpendicular to the magnetic field B, the magnetic force is perpendicular to both v and B and acts like a centripetal force. It has a magnitude q v B.”