The angle of dip at a certain place is `30^(@)`. If the horizontal component of the earth's magnetic field is H, the intensity of the total magnetic field is

Options

A. `(H)/(2) `
B. `(2H)/( sqrt(3))`
C. `H sqrt(2)`
D. `H sqrt(3) `

Answer

To find the intensity of the total magnetic field given the angle of dip and the horizontal component of the Earth's magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Angle of dip (φ) = 30°
- Horizontal component of the Earth's magnetic field (H) = H

2. **Understand the Relationship:**
The intensity of the total magnetic field (B) can be related to the horizontal component (Bh) and the angle of dip (φ) using the formula:
\[ B = \frac{Bh}{\cos \phi} \]

3. **Substitute the Known Values:**
Since the horizontal component \( Bh \) is given as \( H \), we can substitute this into the formula:
\[ B = \frac{H}{\cos 30°} \]

4. **Calculate \( \cos 30° \):**
The value of \( \cos 30° \) is known to be:
\[ \cos 30° = \frac{\sqrt{3}}{2} \]

5. **Substitute \( \cos 30° \) into the Formula:**
Now, substituting \( \cos 30° \) into our equation gives:
\[ B = \frac{H}{\frac{\sqrt{3}}{2}} = H \cdot \frac{2}{\sqrt{3}} \]

6. **Final Result:**
Thus, the intensity of the total magnetic field is:
\[ B = \frac{2H}{\sqrt{3}} \]

### Conclusion:
The intensity of the total magnetic field is \( \frac{2H}{\sqrt{3}} \).