What is the angle of dip at a place where horizontal and vertical components of earth's field are equal?

Options

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

Explanation

To find the angle of dip at a place where the horizontal and vertical components of the Earth's magnetic field are equal, we can follow these steps:

### Step 1: Understand the Components of Earth's Magnetic Field
The Earth's magnetic field can be broken down into two components:
- **B_horizontal**: The horizontal component of the magnetic field.
- **B_vertical**: The vertical component of the magnetic field.

### Step 2: Set Up the Relationship
According to the problem, we know that the horizontal and vertical components are equal:
\[ B_{vertical} = B_{horizontal} \]

### Step 3: Use the Formula for Angle of Dip
The angle of dip (θ) is related to these components by the formula:
\[ \tan(\theta) = \frac{B_{vertical}}{B_{horizontal}} \]

### Step 4: Substitute the Values
Since \( B_{vertical} = B_{horizontal} \), we can substitute this into the formula:
\[ \tan(\theta) = \frac{B_{horizontal}}{B_{horizontal}} = 1 \]

### Step 5: Solve for θ
Now we can solve for θ:
\[ \tan(\theta) = 1 \]
To find θ, we take the inverse tangent (arctan) of 1:
\[ \theta = \tan^{-1}(1) \]

### Step 6: Calculate the Angle
The angle whose tangent is 1 is:
\[ \theta = 45^\circ \]

### Conclusion
Thus, the angle of dip at a place where the horizontal and vertical components of the Earth's magnetic field are equal is:
\[ \theta = 45^\circ \]