(a) A rod of length l is moved horizontal with a uniform velocity `v` in a direction perendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the expression for the emf induced across the end of the rod.
(b) How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.

Explanation

### Solution:

**(a)** To derive the expression for the induced EMF across the ends of the rod, we start by considering the setup:

1. **Setup Description**:
- We have a rod of length \( L \) that is moving horizontally with a uniform velocity \( v \) in a direction perpendicular to its length.
- A uniform magnetic field \( B \) is acting vertically downward.

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