A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It

Options

A. will become rigid showing no movement
B. will stay in any position
C. will stay in North-South direction only
D. will stay in East-West direction only

Answer

To solve the problem regarding the behavior of a compass needle at a geomagnetic pole, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Compass Needle**: A compass needle is a small magnet that aligns itself with the Earth's magnetic field. It can rotate freely in a horizontal plane.

2. **Location of the Geomagnetic Pole**: At the geomagnetic pole, the magnetic field lines of the Earth are directed vertically downwards. This means that the magnetic field is perpendicular to the horizontal plane.

3. **Movement in Horizontal Plane**: The question specifies that the compass needle is allowed to move only in a horizontal plane. This restriction is crucial because it limits the compass needle's ability to respond to the vertical component of the magnetic field.

4. **Direction of Magnetic Field**: At the geomagnetic pole, the magnetic field has no horizontal component. The magnetic field lines are vertical, which means that the compass needle, which is designed to align with the horizontal component of the magnetic field, will not have any horizontal force acting on it.

5. **Conclusion on Compass Needle's Behavior**: Since there is no horizontal magnetic field component to influence the compass needle, it will not align in any specific direction. Instead, it can rest in any position in the horizontal plane, as there is no force to dictate its orientation.

6. **Final Answer**: Therefore, at the geomagnetic pole, the compass needle will stay in any position without a preferred direction.