A current carrying conductor is placed in a magnetic field which is vertically downward. The conductor is oriented horizontally from west to east. The conductor experienced a force ________________.
towards the north.
The force on a current-carrying conductor in a magnetic field is \(\vec{F} = I\vec{L} \times \vec{B}\). Its direction is given by Fleming's left-hand rule: forefinger along the field, middle finger along the current, thumb along the force; the force is perpendicular to both.
Here the current flows from west to east, and the magnetic field points vertically downward. Pointing the forefinger down and the middle finger towards the east, the thumb of the left hand points towards the north.
The force cannot be along east or west, because those lie along the current, and the force is always perpendicular to the current. Of the two horizontal directions perpendicular to the conductor, the rule selects north, not south.
Check: take east = \(\hat{i}\), north = \(\hat{j}\), up = \(\hat{k}\). Then \(\hat{i} \times (-\hat{k}) = -(\hat{i} \times \hat{k}) = -(-\hat{j}) = \hat{j}\), which is north, matching the left-hand rule.
Hence, towards the north.
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