In "Physics for Scientists and Engineers with Modern Physics - 8th Edition", p. 842, it gives the total magnetic force on the segment of current-carrying wire of length $L$ in a uniform magnetic filed:
$$ \vec{F_{B}}= I\vec{L} \times \vec{B} $$
According to Cross Product, it should be this:
But in Fleming's left-hand rule for motors, it says:
Fleming's left-hand rule is used for electric motors, while Fleming's right-hand rule is used for electric generators.
And gives a picture to describe the right-hand-rule:
You see, it's index finger points to the "field", but according to cross product and the above equation, the index finger should point to the direction of the current.
Why they are not same? Am i missed something?