QJEEM23Phbe7a: JEE Main 2023 Physics - Class 12 JEEM23Phbe7a Solution: An emf of is induced in a metal rod of length held normal to a…

The emf induced in a rod moving through a magnetic field is given by Faraday's law of electromagnetic induction, specifically, in the form of motional emf, which states that:

$\text{emf} = B \cdot L \cdot v$

where:

• (B) is the magnetic field strength,
• (L) is the length of the rod, and
• (v) is the velocity of the rod.

In this case, we are given the emf, (B), and (L), and we need to solve for (v). Rearranging the equation gives:

$v = \frac{\text{emf}}{B \cdot L}$

Substituting the given values:

$v = \frac{0.08 \, \text{V}}{0.4 \, \text{T} \times0.1 \, \text{m}} = 2 \, \text{m/s}$