A horizontal conducting rail carries a current from east to west in a uniform magnetic field directed vertically downward. If the rail is free to move, in which direction does the magnetic force act?
The rail accelerates southward, perpendicular to both the current and the magnetic field.
The force on a current-carrying conductor is \(\vec{F} = I\vec{L} \times \vec{B}\), which is perpendicular to both the current and the field.
Take east = +x, north = +y and up = +z. The current flows west, so \(\vec{L} = -\hat{x}\); the field is vertically downward, so \(\vec{B} = -\hat{z}\).
\(\vec{L} \times \vec{B} = (-\hat{x}) \times (-\hat{z}) = \hat{x} \times \hat{z} = -\hat{y}\), i.e. towards the south.
Fleming's left-hand rule confirms it: forefinger down (field), middle finger west (current) — the thumb points south.
The force cannot be upward or downward, since it must be perpendicular to the vertical field, and it cannot be westward, since it must be perpendicular to the current.
Hence, the answer is The rail accelerates southward, perpendicular to both the current and the magnetic field.
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