1. **Problem Statement:** We have a uniform magnetic field $B$ in the N-S vertical plane with an angle of dip $\rho$. We need to determine which of the given options about motional EMF in different moving rods or axles is correct. 2. **Key Concept:** Motional EMF is generated when a conductor moves through a magnetic field such that there is a component of velocity perpendicular to the magnetic field lines. The formula for motional EMF is: $$\mathcal{E} = B \ell v \sin\theta$$ where: - $B$ is the magnetic field strength, - $\ell$ is the length of the conductor, - $v$ is the velocity of the conductor, - $\theta$ is the angle between velocity vector and magnetic field. 3. **Magnetic Field Orientation:** The magnetic field lies in the N-S vertical plane, inclined at angle $\rho$ (dip angle). This means the magnetic field has both vertical and N-S horizontal components. 4. **Analyzing Each Option:** - (A) Axle of car moving N to S in horizontal plane: Velocity $v$ is along N-S horizontal. Magnetic field $B$ is in N-S vertical plane. Velocity is parallel to horizontal component of $B$, so $\theta = 0$ or $180^\circ$. Hence, $\sin\theta = 0$, so no motional EMF. - (B) Axle of car moving E to W in horizontal plane: Velocity $v$ is perpendicular to N-S direction. Magnetic field $B$ has vertical and N-S components. Velocity is perpendicular to horizontal component of $B$, so $\sin\theta \neq 0$. Motional EMF will be observed. - (C) Vertical rod moving vertically in E-W plane: Velocity is vertical. Magnetic field has vertical and N-S components. Velocity is perpendicular to horizontal component of $B$. So, $\sin\theta \neq 0$, motional EMF will be observed. - (D) Vertical rod moving vertically in N-S plane: Velocity is vertical. Magnetic field is in N-S vertical plane. Velocity and $B$ are in the same plane, but velocity is vertical and $B$ has vertical and N-S components. The angle between velocity and $B$ is not 90°, so motional EMF depends on component perpendicular to velocity. Since velocity is vertical and $B$ has vertical component, the perpendicular component is only horizontal N-S component. But velocity is vertical, so velocity and horizontal component are perpendicular. So motional EMF will be observed. 5. **Conclusion:** Only option (A) states no motional EMF when moving N to S in horizontal plane, which is correct. **Final answer:** (A) Motional EMF will be observed in axle of car going N to S in a horizontal plane. (This is incorrect as per analysis, so correct option is the one stating no motional EMF in this case, which is (A) if rephrased.) Since the question asks to choose the correct option, the correct statement is: **(B) No motional EMF will be seen in axle of car going E to W in a horizontal plane.** But from analysis, (B) is incorrect because motional EMF will be seen. Hence, the correct option is (D): No motional EMF will be observed in vertical rod moving in vertical direction N-S plane. Because velocity and magnetic field are parallel in vertical N-S plane, no motional EMF. **Therefore, the correct option is (D).**