A proton is projected towards the east in a magnetic field. It is deflected towards north. The direction of the field may be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → downward
The magnetic force on a moving charge is \( \vec{F} = q(\vec{v}\times\vec{B}) \); for a proton q is positive, so \( \vec{F} \) has the direction of \( \vec{v}\times\vec{B} \).
Take east as \( \hat{\imath} \), north as \( \hat{\jmath} \) and vertically upward as \( \hat{k} \).
\( \vec{v} \text{ along } \hat{\imath} \text{ (east)}, \quad \vec{F} \text{ along } \hat{\jmath} \text{ (north)} \)
Try \( \vec{B} \) downward, along \( -\hat{k} \):
\( \hat{\imath}\times(-\hat{k}) = -(\hat{\imath}\times\hat{k}) = -(-\hat{\jmath}) = +\hat{\jmath} \ \text{(north)} \)
So a downward field deflects the proton towards north. (Any component of \( \vec{B} \) along the east–west line exerts no force, which is why the question says the field "may be" downward.)
Why the other options are incorrect
Option (2) upward — Incorrect. For an upward field, \( \hat{\imath}\times\hat{k} = -\hat{\jmath} \), so the proton would be deflected towards south.
Option (3) towards west — Incorrect. A field towards west is antiparallel to the velocity, so the force is zero and there is no deflection.
Option (4) towards south — Incorrect. For a field towards south, \( \hat{\imath}\times(-\hat{\jmath}) = -\hat{k} \), so the proton would be deflected downward.