Given below are two statements
Statement I : magnetic field does zero work on a charge particle entering with uniform velocity.
Statement II : A charge particle entering a region of uniform magnetic field with its velocity perpendicular to the direction of magnetic field, executes a circular motion.
In the light of the above statement, choose the most appropriate answer from the options given below
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both statement I and statement II are correct
The magnetic force on a moving charge is the Lorentz force \( \vec{F} = q\,\vec{v}\times\vec{B} \), which is always perpendicular to the velocity.
Statement I magnetic field does zero work on a charge particle entering with uniform velocity. — Correct. Since the force is perpendicular to the velocity, it is perpendicular to every small displacement, so the work done is zero and the speed (kinetic energy) of the charge does not change.
\( \displaystyle W = \int \vec{F}\cdot d\vec{s} = \int (q\,\vec{v}\times\vec{B})\cdot\vec{v}\,dt = 0 \)
Statement II A charge particle entering a region of uniform magnetic field with its velocity perpendicular to the direction of magnetic field, executes a circular motion. — Correct. With \( \vec{v} \perp \vec{B} \), the force has a constant magnitude \( qvB \) and always points at right angles to the velocity, so it acts as a centripetal force and the charge moves in a circle of radius \( r = mv/(qB) \).
NCERT (2026-27):
Motion in a Magnetic Field – “… In the case of motion of a charge in a magnetic field, the magnetic force is perpendicular to the velocity of the particle. So no work is done and no change in the magnitude of the velocity is produced (though the direction of momentum may be changed). … First consider the case of v perpendicular to B. The perpendicular force, q v × B, acts as a centripetal force and produces a circular motion perpendicular to the magnetic field.”