At certain places, if horizontal and vertical components of earth's magnetic field are equal then the angle of dip is:

Options

A. `0^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Explanation

To find the angle of dip when 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 resolved into two components:
- The horizontal component (Bh)
- The vertical component (Bv)

### Step 2: Set Up the Relationship
Given that the horizontal and vertical components are equal, we can express this mathematically:
\[ Bh = Bv \]

### Step 3: Use the Definitions of the Components
The horizontal and vertical components can also be expressed in terms of the total magnetic field (B) and the angle of dip (δ):
- \( Bh = B \cos(δ) \)
- \( Bv = B \sin(δ) \)

### Step 4: Set the Components Equal
Since we know that \( Bh = Bv \), we can substitute the expressions from Step 3:
\[ B \cos(δ) = B \sin(δ) \]

### Step 5: Simplify the Equation
Assuming \( B \neq 0 \), we can divide both sides by B:
\[ \cos(δ) = \sin(δ) \]

### Step 6: Use Trigonometric Identity
The equation \( \cos(δ) = \sin(δ) \) can be rewritten using the tangent function:
\[ \tan(δ) = 1 \]

### Step 7: Solve for the Angle of Dip
The angle whose tangent is 1 is:
\[ δ = 45^\circ \]

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