Horizontal component of earth's field at a height of 1 m from the surface of earth is H. Its value at a height of 10 m from surface of earth is

Options

A. `H//10`
B. `H//9`
C. `H//100`
D. H

Answer

To solve the question regarding the horizontal component of Earth's magnetic field at different heights, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We are given that the horizontal component of Earth's magnetic field at a height of 1 meter from the surface of the Earth is \( H \). We need to find its value at a height of 10 meters from the surface of the Earth.

2. **Concept of Horizontal Component**: The horizontal component of the Earth's magnetic field is relatively constant over small vertical distances above the Earth's surface. This means that for small changes in height, the horizontal component does not vary significantly.

3. **Identifying the Heights**: We have two heights to consider:
- Height 1: \( h_1 = 1 \, \text{m} \) where the magnetic field is \( H \).
- Height 2: \( h_2 = 10 \, \text{m} \) where we need to find the magnetic field.

4. **Applying the Concept**: Since the height difference (from 1 m to 10 m) is small relative to the radius of the Earth (approximately 6400 km), we can assume that the horizontal component of the magnetic field remains approximately the same.

5. **Conclusion**: Therefore, the value of the horizontal component of the Earth's magnetic field at a height of 10 meters from the surface of the Earth will also be \( H \).

### Final Answer:
The horizontal component of Earth's magnetic field at a height of 10 meters from the surface of the Earth is \( H \).

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