The place where horizontal and vertical component of earth's magnetic field are equal to the only of dip is:

Options

A. `90^(@)`
B. `45^(@)`
C. `33 (1)/(2)""^(@)`
D. `70^(@)`

Explanation

To solve the problem, we need to find the angle of dip (θ) where the horizontal component (Bh) and the vertical component (Bv) of the Earth's magnetic field are equal.

### Step-by-Step Solution:

1. **Understanding the Components of Earth's Magnetic Field**:
- The Earth's magnetic field can be broken down into two components: the horizontal component (Bh) and the vertical component (Bv).
- The angle of dip (θ) is defined as the angle made by the resultant magnetic field with the horizontal plane.

2. **Using the Formula for Angle of Dip**:
- The tangent of the angle of dip (θ) is given by the formula:
\[ \tan(\theta) = \frac{Bv}{Bh} \]

3. **Setting the Components Equal**:
- According to the problem, we are given that the vertical component (Bv) is equal to the horizontal component (Bh):
\[ Bv = Bh \]

4. **Substituting into the Formula**:
- Substituting Bv = Bh into the formula for the tangent of the angle of dip:
\[ \tan(\theta) = \frac{Bv}{Bh} = \frac{Bh}{Bh} = 1 \]

5. **Finding the Angle**:
- The angle whose tangent is 1 is:
\[ \theta = \tan^{-1}(1) = 45^\circ \]

6. **Conclusion**:
- Therefore, the angle of dip (θ) where the horizontal and vertical components of the Earth's magnetic field are equal is:
\[ \theta = 45^\circ \]

### Final Answer:
The place where the horizontal and vertical components of Earth's magnetic field are equal corresponds to an angle of dip of **45 degrees**.

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