At what positions, the neutral points will lie for a bar magnet when magnetic axis of magnet is lying in the magnetic meridian
(i) with N-pole of magnet pointing North
(ii) with S-pole of magnet pointing North?

Options

A. the earth's magnetic field is zero
B. the magnet's magnetic field is zero
C. the fields of the magnet and the earth are equal and in the same direction
D. the fields of the magnet and the earth are equal and in opposite direction

Answer

To determine the positions of the neutral points for a bar magnet when its magnetic axis is lying in the magnetic meridian, we will analyze two scenarios:

1. When the North pole of the magnet is pointing North (geographical North).
2. When the South pole of the magnet is pointing North (geographical North).

### Step-by-Step Solution:

#### Case (i): North Pole of the Magnet Pointing North

1. **Understanding Neutral Points**: Neutral points are locations where the magnetic field due to the bar magnet (B) cancels out the Earth's magnetic field (B_H). At these points, the net magnetic field is zero.

2. **Magnetic Field Directions**:
- The magnetic field due to a bar magnet originates from its North pole and terminates at its South pole.
- When the North pole of the magnet is pointing North, the direction of the magnetic field lines from the magnet will be directed away from the North pole towards the South pole.

3. **Earth's Magnetic Field**: The Earth's magnetic field also has a direction, which is from the magnetic North pole (near the geographical North pole) to the magnetic South pole.

4. **Finding Neutral Points**:
- The neutral points will occur where the magnetic field due to the bar magnet (B) is equal in magnitude but opposite in direction to the Earth's magnetic field (B_H).
- This balance occurs along the axis of the magnet, specifically at two points:
- One point is located on the axis of the magnet, beyond the North pole (let's call it P1).
- Another point is located on the axis of the magnet, beyond the South pole (let's call it P2).

5. **Conclusion for Case (i)**: The neutral points will lie along the axial line of the magnet, one on each side of the magnet.

#### Case (ii): South Pole of the Magnet Pointing North

1. **Understanding the Configuration**: In this case, the South pole of the magnet is directed towards geographical North.

2. **Magnetic Field Directions**:
- The magnetic field lines from the bar magnet will now be directed from the North pole (geographical North) towards the South pole of the magnet.
- Since the South pole of the magnet is pointing North, the magnetic field produced by the magnet will be directed towards the South pole.

3. **Earth's Magnetic Field**: The direction of the Earth's magnetic field remains unchanged.

4. **Finding Neutral Points**:
- Here, the magnetic field due to the bar magnet (B) and the Earth's magnetic field (B_H) are in the same direction.
- The neutral points will occur along the equatorial plane of the magnet, where the repulsive forces will cancel each other out.
- Specifically, there will be two neutral points:
- One point will be located above the magnet (let's call it Q1).
- Another point will be located below the magnet (let's call it Q2).

5. **Conclusion for Case (ii)**: The neutral points will lie along the equatorial line of the magnet, one above and one below the magnet.

### Final Summary:
- **For Case (i)**: Neutral points are located at axial positions (one on each side of the magnet).
- **For Case (ii)**: Neutral points are located at equatorial positions (one above and one below the magnet).