# Motional EMF from Lorentz force class 12

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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.

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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1. What is the motional emf formula?

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2. Which force on the moving free electrons that maintains the potential difference and produces the EMF

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3. The potential difference between the two ends Q and P are

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4. The accumulation of charges at the two ends continues till these two forces

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5. Derivation of Motional EMF from Lorentz force consider

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