The angle of dip at a certain place on earth is `60^@` and the magnitude of the earth's horizontal component of the magnetic field is 0.26 G . The magnetic field at the place on earth is

Options

A. 0.13 G
B. 0.26 G
C. 0.52 G
D. 0.65 G

Answer

To find the magnetic field at a certain place on Earth given the angle of dip and the horizontal component of the magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Angle of dip (θ) = 60°
- Horizontal component of magnetic field (Bh) = 0.26 G

2. **Understand the Relationship:**
The relationship between the total magnetic field (B) and the horizontal component (Bh) is given by:
\[ Bh = B \cdot \cos(\theta) \]
where θ is the angle of dip.

3. **Substitute the Known Values:**
Substitute the known values into the equation:
\[ 0.26 = B \cdot \cos(60°) \]

4. **Calculate cos(60°):**
We know that:
\[ \cos(60°) = \frac{1}{2} \]
Therefore, the equation becomes:
\[ 0.26 = B \cdot \frac{1}{2} \]

5. **Solve for B:**
To find B, multiply both sides of the equation by 2:
\[ B = 0.26 \cdot 2 \]
\[ B = 0.52 \, \text{G} \]

6. **Conclusion:**
The magnetic field at the place on Earth is:
\[ B = 0.52 \, \text{G} \]

### Final Answer:
The magnetic field at the place on Earth is **0.52 G**.

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