In this short piece of article, we will discuss and derive an expression for motional EMF from Lorentz force class 12, so let’s get started…
Motional EMF from Lorentz force
As we know that a conductor has large numbers of free electrons. When it moves through a magnetic field, a Lorentz force acting on the free electrons can set up a current. The below figure shows a rectangular conductor in which arm PQ is free to move.
It is placed in the uniform magnetic field B and directed normally into the plane of the paper. As the arm, PQ is moved towards the left with the velocity $v$, the free electrons of PQ also move at the same speed towards the left.
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The electrons experience a magnetic Lorentz force, $F_m =qvB$. According to the fleming’s left-hand rule, this force act in the direction of QP, and hence, the free electrons will move towards P. A negative charge accumulates at P and a positive charge at Q.
An electric field $E$ is set up in the conductor from Q to P. This field exerts a force, $F_e = qE$ on the free electrons. The accumulation of charges at the two ends continues till these two forces balance each other. i.e $$F_m = F_e$$ Or $$qvB=qE\quad or\quad vB=E$$
The potential difference between the two ends Q and P are $$ V=El=Blv$$ Clearly, it is the magnetic force on the moving free electrons that maintains the potential difference and produce the EMF $${\mathcal {E}} = Blv$$ As this EMF generated due to the motion of the conductor, so it is called motional EMF.
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