A long straight wire lies on a horizontal table. It carries a steady current from east to west. At that place, the horizontal component of the earth’s magnetic field points from geographic south to geographic north. The magnetic force on the wire due to this horizontal field is directed
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → vertically downwards
The force on a straight current-carrying wire is \(\vec{F}=I\vec{l}\times\vec{B}\). It acts at right angles to both the wire and the field. Take east as \(+x\), north as \(+y\) and vertically up as \(+z\). The current is towards the west, so \(\vec{l}\) is along \(-\hat{i}\). The field is along \(+\hat{j}\).
\( (-\hat{i})\times\hat{j}=-\hat{k} \)
From the above, the force is along \(-\hat{k}\). Hence, it points vertically down.
Option (1) vertically upwards — Incorrect. This is the direction for a current from west to east. Reversing the current reverses the force.
Option (2) vertically downwards — Correct. \(\vec{l}\times\vec{B}\) is along \(-\hat{k}\) when the current flows towards the west and the field points north.
Option (3) towards the north — Incorrect. North is the direction of the field itself. The magnetic force is always at right angles to the field.
Option (4) towards the south — Incorrect. South is also along the line of the field. A force along the field line would need \(\vec{l}\times\vec{B}\) to lie along \(\vec{B}\), which never happens.
NCERT (2026-27):
Example 4.9 – “(a) When the current is flowing from east to west, θ = 90° … The direction of the force is downwards. This direction may be obtained by the directional property of cross product of vectors.”