Motional EMF is the potential difference produced across the length of a conductor moving in a Magnetic Field. Suppose a conductor of length l is moving with a velocity v in a uniform magnetic field B as shown in figure below.
As the conductor is having mobile electrons which can move freely, therefore we can say that electrons of conductor is also moving with a speed of v in an external magnetic field B.
Therefore, force experienced by the electrons F = e (vxB), here bold letter means vector form.
Form the basic knowledge of cross product of two vectors; we can conclude that the direction of force on the electrons of conductor will be upward. Because of this upward force on electrons, electrons of conductor will start accumulating at the upper portion A of conductor.
Since the movement of electron in in upward direction, therefore we can say that positive charge of the conductor is moving downward. Mind that positive charges do not move actually rather because of movement of electrons positive charge will be left behind and hence we can assume that positive charge is moving downward and accumulating at lower portion B of the conductor.
Because of this accumulation of positive and negative charge at point A and B, an Electric Field will be developed inside the conductor whose strength will depend on the strength of charge accumulated. Let us assume that +Q and –Q charge accumulated at point A and B & the strength of Electric Field is E. Mind here that, direction of Electric Field will be from B to A i.e. in upward direction (Direction of Electric Field is from positive to negative charge).
Thus Force because of Magnetic Field and Electric Field are opposing each other and electron will continue to move toward A till the Electric Force and magnetic Force balances each other. At equilibrium condition,
Electric Force on electron = Magnetic Force on electron and no further movement of electron.
Therefore, eE = evB
Hence, E = vB ………………………………..(1)
Potential Difference between A and B i.e. EMF = E.l
As this potential difference is because of movement of conductor in a magnetic field, this is popularly known as Motional EMF.
So, for a conductor of length l, moving with a velocity v in a uniform magnetic field B, the motional EMF = vBl