How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.

Explanation

Let `vecB=B(-hatk)` (in the negative z-direction) The rod PQ is moved towards right, i.e., in the y-direction. So, the charge carriers (electrons) in the rod moves also in the y-direction with a velocity,
`vecv=vhatj`
As the charge of an electron is -e, the Lorentz magnetic force acting on it is
`vecF=-ehatvxxvecB=-e[vhatjxxB(-hatk)]=evBhati`
So, the electron drift in the rod PQ is in the x-direction, i.e., from P to Q. Then, as per convention, the motional emf in PQ will be directed from Q to P. This is the direction obtained by applying Flemings right hand rule.