A metal rod is falling toward the surface of the Earth near the equator. As it falls, one end of the rod become positively charged due to the motional emf of the rod through the Earth's magnetic field. The rod is oriented so that

Options

A. The rod is horizontal with the positive end toward the west
B. The rod is vertical with the positive end toward the north
C. The rod is vertical with the positive end higher
D. The rod is horizontal with the positive end toward the east

Answer

To solve the problem, we need to analyze the situation of a metal rod falling towards the Earth near the equator and how it interacts with the Earth's magnetic field.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a metal rod falling towards the Earth's surface.
- The rod is falling near the equator, where the Earth's magnetic field is approximately horizontal and directed from geographic south to geographic north.

2. **Direction of Motion**:
- As the rod falls, it moves downward due to gravity. This motion is vertical.

3. **Earth's Magnetic Field**:
- Near the equator, the Earth's magnetic field lines run horizontally. The magnetic field direction is from the magnetic south to the magnetic north, which is approximately aligned with the geographic north.

4. **Induced EMF and Charge Separation**:
- According to Faraday's law of electromagnetic induction, when a conductor moves through a magnetic field, an electromotive force (emf) is induced in the conductor.
- The direction of the induced emf can be determined using the right-hand rule. If we point our thumb in the direction of the velocity of the rod (downward) and our fingers in the direction of the magnetic field (from south to north), our palm will face the direction of the induced positive charge.

5. **Applying the Right-Hand Rule**:
- With the rod falling downward (thumb pointing down) and the magnetic field pointing from south to north (fingers pointing north), the palm faces towards the west. This indicates that the end of the rod that is moving downwards will become positively charged towards the west.

6. **Conclusion**:
- Therefore, as the rod falls, the end of the rod that is oriented towards the west becomes positively charged. The rod is oriented horizontally with the positive end towards the west.

### Final Answer:
The rod is horizontal with the positive end towards the west.