The vertical and horizontal components of earth's magnetic at a place are `0.2` G and `0.3464` G respectively . Calculate the angle of dip and earth's magnetic field at that place .

Answer

To solve the problem of calculating the angle of dip and the total Earth's magnetic field at a given location, we can follow these steps:

### Step 1: Identify the Given Values
We have the following components of Earth's magnetic field:
- Vertical component, \( B_V = 0.2 \, \text{G} \)
- Horizontal component, \( B_H = 0.3464 \, \text{G} \)

### Step 2: Calculate the Angle of Dip
The angle of dip \( \theta \) (or \( \rho \)) can be calculated using the formula:
\[ \tan(\theta) = \frac{B_V}{B_H} \]
Substituting the given values:
\[ \tan(\theta) = \frac{0.2}{0.3464} \]

### Step 3: Calculate the Value of \( \tan(\theta) \)
Now, we perform the division:
\[ \tan(\theta) = \frac{0.2}{0.3464} \approx 0.576 \]

### Step 4: Calculate the Angle \( \theta \)
To find \( \theta \), we take the arctangent (inverse tangent) of the result:
\[ \theta = \tan^{-1}(0.576) \]
Using a calculator, we find:
\[ \theta \approx 29.74^\circ \]

### Step 5: Calculate the Total Earth's Magnetic Field
The total Earth's magnetic field \( B \) can be calculated using the Pythagorean theorem:
\[ B = \sqrt{B_V^2 + B_H^2} \]
Substituting the values:
\[ B = \sqrt{(0.2)^2 + (0.3464)^2} \]
Calculating the squares:
\[ B = \sqrt{0.04 + 0.1209} = \sqrt{0.1609} \]
Calculating the square root:
\[ B \approx 0.4011 \, \text{G} \]

### Final Results
- Angle of dip \( \theta \approx 29.74^\circ \)
- Total Earth's magnetic field \( B \approx 0.4011 \, \text{G} \)

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