The horizontal and vertical components of earth's magnetic field at a place are 0.3G and 0.52G. The earth's magnetic field and the angle of dip are

Options

A. `0.3g and delta=30^(@)`
B. `0.4g and delta=40^(@)`
C. `0.5g and delta=50^(@)`
D. `0.6g and delta=60^(@)`

Explanation

To solve the problem of finding the Earth's magnetic field and the angle of dip given the horizontal and vertical components, we can follow these steps:

### Step 1: Identify the Components
We are given:
- Horizontal component (Bh) = 0.3 G
- Vertical component (Bv) = 0.52 G

### Step 2: Calculate the Magnitude of the Earth's Magnetic Field
The magnitude of the Earth's magnetic field (B) can be calculated using the Pythagorean theorem:
\[ B = \sqrt{B_h^2 + B_v^2} \]
Substituting the values:
\[ B = \sqrt{(0.3)^2 + (0.52)^2} \]
Calculating the squares:
\[ B = \sqrt{0.09 + 0.2704} = \sqrt{0.3604} \]
Calculating the square root:
\[ B \approx 0.6 \, G \]

### Step 3: Calculate the Angle of Dip
The angle of dip (δ) can be calculated using the formula:
\[ \tan(δ) = \frac{B_v}{B_h} \]
Substituting the values:
\[ \tan(δ) = \frac{0.52}{0.3} \]
Calculating the division:
\[ \tan(δ) \approx 1.7333 \]
Now, to find the angle δ, we take the arctangent:
\[ δ = \tan^{-1}(1.7333) \]
Calculating the angle:
\[ δ \approx 60^\circ \]

### Final Result
Thus, the magnitude of the Earth's magnetic field is approximately **0.6 G** and the angle of dip is **60 degrees**.

### Summary
- Earth's Magnetic Field (B) = 0.6 G
- Angle of Dip (δ) = 60°