The vertical component of earth's magnetic field at a place is `sqrt3` times the horizontal component the value of angle of dip at this place is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `75^(@)`

Explanation

To find the angle of dip (θ) when the vertical component of Earth's magnetic field (BV) is \(\sqrt{3}\) times the horizontal component (BH), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**:
We know that the vertical component (BV) is related to the horizontal component (BH) through the angle of dip (θ) using the formula:
\[ BV = BH \cdot \tan(\theta) \]

2. **Substitute the Given Values**:
According to the problem, we have:
\[ BV = \sqrt{3} \cdot BH \]
Now, substituting this into the formula gives:
\[ \sqrt{3} \cdot BH = BH \cdot \tan(\theta) \]

3. **Simplify the Equation**:
We can divide both sides of the equation by BH (assuming BH ≠ 0):
\[ \sqrt{3} = \tan(\theta) \]

4. **Find the Angle θ**:
To find θ, we take the inverse tangent (arctan) of both sides:
\[ \theta = \tan^{-1}(\sqrt{3}) \]

5. **Determine the Value of θ**:
From trigonometric values, we know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore:
\[ \theta = 60^\circ \]

### Final Answer:
The angle of dip at this place is \(60^\circ\).

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