1. Given data

• Length of rod: $l = 20\text{ cm} = 0.20\text{ m}$
• Speed of rod: $v = 20\text{ m/s}$
• Horizontal component of Earth’s magnetic field: $B_H = 4\times 10^{-3}\text{ T}$
• Angle of dip: $\delta = 45^\circ$

2. Direction analysis

• Rod is placed in North-South direction.
• Rod moves towards East.
• Earth’s magnetic field lies in the North-vertical plane.

The horizontal component $B_H$ is along North. The vertical component is

Since $\delta = 45^\circ$,

3. Which component produces motional emf?

Motional emf across the rod is due to

• $\vec l$ is along North-South.
• $\vec v$ is towards East.

Now check magnetic field components:

• For horizontal field $B_H$ (towards North):

  $$\vec v \times \vec B_H = \text{East} \times \text{North} = \text{vertical}$$

  This is perpendicular to the rod, so it does not contribute to emf along the rod.

• For vertical field $B_V$ (downward):

  $$\vec v \times \vec B_V = \text{East} \times \text{downward} = \text{North/South direction}$$

  This is along the rod, so it contributes fully.

Hence,

4. Substitute values

First,

So,

5. Final answer

The induced emf is