What is the angle of dip at a place where the horizontal component `(B_(H))` and vertical component `(B_(v))` of earth.s magnetic field are equal:

Options

A. `130^(@)`
B. `60^(@)`
C. `45^(@)`
D. `90^(@)`

Explanation

To solve the problem, we need to find the angle of dip (φ) at a location where the horizontal component (B_H) and the vertical component (B_V) of the Earth's magnetic field are equal.

### Step-by-Step Solution:

1. **Understanding the Components of the Magnetic Field**:
- The Earth's magnetic field can be resolved into two components: the horizontal component (B_H) and the vertical component (B_V).
- The angle of dip (φ) is defined as the angle between the direction of the Earth's magnetic field and the horizontal plane.

2. **Setting Up the Equation**:
- We know that the angle of dip can be expressed using the tangent function:
\[ \tan(φ) = \frac{B_V}{B_H} \]
- In this case, we are given that the horizontal component (B_H) and the vertical component (B_V) are equal:
\[ B_H = B_V \]

3. **Substituting the Values**:
- Since \(B_H = B_V\), we can substitute this into the equation:
\[ \tan(φ) = \frac{B_V}{B_H} = \frac{B_H}{B_H} = 1 \]

4. **Finding the Angle**:
- Now, we need to find the angle whose tangent is 1:
\[ φ = \tan^{-1}(1) \]
- The value of \(tan^{-1}(1)\) is known to be:
\[ φ = 45^\circ \]

5. **Conclusion**:
- Therefore, the angle of dip at the place where the horizontal and vertical components of the Earth's magnetic field are equal is:
\[ φ = 45^\circ \]

### Final Answer:
The angle of dip is **45 degrees** (Option C).