An electron moves horizontally from geographic south to geographic north in a magnetic field, which is vertically downward. The electron is deflected towards
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → East
The magnetic Lorentz force on a moving charge is \( \vec{F} = q(\vec{v}\times\vec{B}) \), with q = −e for an electron. Take east as \( \hat{\imath} \), north as \( \hat{\jmath} \) and vertically up as \( \hat{k} \).
\( \vec{v} = v\,\hat{\jmath} \)
\( \vec{B} = -B\,\hat{k} \)
\( \vec{v}\times\vec{B} = v\hat{\jmath} \times (-B\hat{k}) = -vB\,\hat{\imath} \)
\( \vec{F} = -e(\vec{v}\times\vec{B}) = +evB\,\hat{\imath} \)
The force is along \( +\hat{\imath} \), so the electron is deflected towards the east.
Why the other options are incorrect
Option (1) West — Incorrect. West is the direction of \( \vec{v}\times\vec{B} \), which is the deflection of a positive charge; the negative charge of the electron reverses it.
Option (2) North — Incorrect. The magnetic force is always perpendicular to the velocity, so it cannot act along the direction of motion.
Option (4) South — Incorrect. The magnetic force cannot act opposite to the velocity either.