An electron is projected in a uniform magnetic field along the direct…

The correct answer is Option (3) → no force in magnetic field

The magnetic force on a moving charge is the Lorentz force

    \( \displaystyle \vec{F} = q\,(\vec{v}\times\vec{B}), \qquad F = q v B\sin\theta \)

For motion along the field, the angle between \( \vec{v} \) and \( \vec{B} \) is \( 0^\circ \), so \( \sin\theta = 0 \) and

    \( \displaystyle F = q v B \sin 0^\circ = 0 \)

The electron experiences no force and continues in a straight line with the same velocity.

Option (1) a force opposite to the magnetic field — Incorrect. A magnetic force is never along or opposite to \( \vec{B} \), because it is a cross product with \( \vec{B} \).

Option (2) a force in the direction of magnetic field — Incorrect. Same reason: the force \( q(\vec{v}\times\vec{B}) \) is always perpendicular to \( \vec{B} \).

Option (3) no force in magnetic field — Correct. \( \vec{v} \) parallel to \( \vec{B} \) gives \( \vec{v}\times\vec{B} = 0 \).

Option (4) a force perpendicular to the magnetic field — Incorrect. A perpendicular force acts only when \( \vec{v} \) has a component perpendicular to \( \vec{B} \); here it has none.

NCERT (2026-27):
Magnetic Field, Lorentz Force – “… (ii) The magnetic force \( q\,[\,\mathbf{v} \times \mathbf{B}\,] \) includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel.”