A positively charged particle (an alpha particle) projected towards the west is deflected towards the north by a magnetic field. What is the direction of the magnetic field?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Upward
The magnetic force on a moving charge is \( \vec{F}=q\,(\vec{v}\times\vec{B}) \), perpendicular to both the velocity and the field. Take east as \( \hat{\imath} \), north as \( \hat{\jmath} \) and upward as \( \hat{k} \). The alpha particle is positive, moves west (\( \vec{v} \) along \( -\hat{\imath} \)) and is pushed north (\( \vec{F} \) along \( +\hat{\jmath} \)).
Option (1) Towards the south — Incorrect. \( (-\hat{\imath})\times(-\hat{\jmath})=+\hat{k} \), so this field would push the particle upward. But the particle is deflected towards the north.
Option (2) Towards the east — Incorrect. A field towards the east lies along the line of the velocity (opposite to it), and \( \vec{v}\times\vec{B}=0 \), so there would be no force at all.
Option (3) Downward — Incorrect. \( (-\hat{\imath})\times(-\hat{k})=-\hat{\jmath} \), so this field would deflect the particle towards the south.
Option (4) Upward — Correct. \( (-\hat{\imath})\times\hat{k}=+\hat{\jmath} \), so with \( \vec{B} \) vertically upward the force on the positive charge points north.