A horizontal wire is carrying current from south to north direction. The direction of magnetic field at a point just below wire is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Westward
The direction of the field of a straight current is given by the right-hand thumb rule, or by \( d\vec{B} \propto d\vec{l}\times\hat{r} \) from the Biot-Savart law, where \( \hat{r} \) points from the wire to the point.
Take east as \( +\hat{\imath} \), north as \( +\hat{\jmath} \) and vertically up as \( +\hat{k} \). The current flows north and the point is just below the wire.
\( d\vec{l} \text{ along } +\hat{\jmath} \)
\( \hat{r} = -\hat{k} \)
\( d\vec{l}\times\hat{r} = \hat{\jmath}\times(-\hat{k}) = -\hat{\imath} \)
The field just below the wire points west.