A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at `22^(@)` with the horizontal . The horizontal componemt of the earth's magnetic field at the place is know to be 0.35 G . Determine the magnitude of the earth's magnetic field at the place .

Explanation

To determine the magnitude of the Earth's magnetic field at the place where the magnetic needle is pointing down at an angle of dip of \(22^\circ\) with the horizontal, we can use the relationship between the horizontal and vertical components of the magnetic field.

### Step-by-Step Solution:

1. **Identify the Components of the Magnetic Field:**
- The horizontal component of the Earth's magnetic field (\(B_H\)) is given as \(0.35 \, \text{G}\).
- The angle of dip (\(\theta\)) is given as \(22^\circ\).

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