Generation of Force with Conductor in a Magnetic Field

When a conductor of length $l$, carrying a current $i$, is placed in a magnetic field $B$, a force will be exerted on it which is given by:

$$\vec{F}=\vec{i}l\times \vec{B}$$

In order to maximize the magnitude of the developed force, for a given current, conductor length, and magnetic flux density, the structure of electric machines are designed such that:

$$\vec{i}\perp \vec{B}⟶|\vec{i}l\times \vec{B}|=i\times l\times B\times \sin (90°)=ilB$$

Right-hand Rule

The direction of the force $\vec{F}$ can be found by using right-hand fingers. If you point your right-hand fingers in the direction of $\vec{i}$, and wrap your fingers towards the direction of $\vec{B}$, your thumb will be pointing to $\vec{F}$.