A beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off and the same magnetic field is maintained, what is the shape of the trajectory of the electrons?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Circular
The beam goes undeflected because the electric force \( eE \) and the magnetic force \( evB \) on each electron are equal and opposite. For this, the velocity must be perpendicular to \( \vec{B} \). With the electric field off, only the magnetic force \( -e\,\vec{v}\times\vec{B} \) acts. It is always perpendicular to the velocity.
Option (1) Straight line — Incorrect. A straight path needs zero net force, but the magnetic force \( evB \) is no longer balanced once the electric field is off.
Option (2) Parabolic — Incorrect. A parabola is the path under a constant force in a fixed direction, as in a uniform electric field. The magnetic force changes direction as the velocity turns.
Option (3) Elliptical — Incorrect. A force perpendicular to the velocity does no work. So the speed and the force \( evB \) stay constant. The radius of the path, \( r=mv/eB \), then stays fixed, while on an ellipse it would change.
Option (4) Circular — Correct. The magnetic force has a constant size and stays perpendicular to the velocity. It acts as a centripetal force, so the electrons move in a circle in the plane perpendicular to \( \vec{B} \).
NCERT (2026-27):
Motion in a Magnetic Field – “We shall consider motion of a charged particle in a uniform magnetic field. 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.”