A beam of electrons move horizontally from South to North in the region of the magnetic field acting vertically downward. The force acting on the electron due to the magnetic field is directed:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → towards the east
The Lorentz magnetic force on a charge \( q \) moving with velocity \( \vec{v} \) in a field \( \vec{B} \) is \( \vec{F} = q(\vec{v} \times \vec{B}) \). It is perpendicular to both \( \vec{v} \) and \( \vec{B} \), and for a negative charge it is opposite to \( \vec{v} \times \vec{B} \).
Take East as \( \hat{\imath} \), North as \( \hat{\jmath} \) and vertically up as \( \hat{k} \).
\( \vec{v} = v\,\hat{\jmath} \text{ (north)}, \quad \vec{B} = -B\,\hat{k} \text{ (downward)} \)
\( \vec{v} \times \vec{B} = vB\,(\hat{\jmath} \times (-\hat{k})) = -vB\,\hat{\imath} \text{ (west)} \)
For an electron \( q = -e \), so the force is along \( +\hat{\imath} \), towards the east.
Why the other options are incorrect
Option (1) vertically downward — Incorrect. The magnetic force is perpendicular to the field, so it cannot be along the vertical field.
Option (2) vertically upward — Incorrect. For the same reason, no vertical force acts.
Option (4) towards the west — Incorrect. West is the direction of the force on a positive charge; the electron's negative charge reverses it.
NCERT (2026-27):
Magnetic Field, Lorentz Force – “… (i) It depends on q, v and B (charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge.”
Magnetic Field, Lorentz Force – “… The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field.”