At a certain place the angle of dip is `30^(@)` and the horizontal component of earth's magnetic field is `0.50` oersted. The earth's total magnetic field is

Options

A. `sqrt(3)`
B. 1
C. `1//sqrt(3)`
D. `(1)/(2)`

Explanation

To find the total magnetic field (B) at a certain place where the angle of dip (δ) is 30 degrees and the horizontal component of the Earth's magnetic field (Bh) is 0.50 oersted, we can use the relationship between the total magnetic field, the horizontal component, and the angle of dip.

### Step-by-Step Solution:

1. **Understand the relationship**: The horizontal component of the Earth's magnetic field is related to the total magnetic field and the angle of dip by the formula:
\[ B_h = B \cdot \cos(δ) \]
where:
- \(B_h\) is the horizontal component of the magnetic field,
- \(B\) is the total magnetic field,
- \(δ\) is the angle of dip.

2. **Rearrange the formula**: To find the total magnetic field \(B\), we can rearrange the formula:
\[ B = \frac{B_h}{\cos(δ)} \]

3. **Substitute the known values**: We know that:
- \(B_h = 0.50\) oersted,
- \(δ = 30^\circ\).

We also know that:
\[ \cos(30^\circ) = \frac{\sqrt{3}}{2} \]

Now substitute these values into the formula:
\[ B = \frac{0.50}{\cos(30^\circ)} = \frac{0.50}{\frac{\sqrt{3}}{2}} \]

4. **Simplify the expression**: To simplify the expression, multiply by the reciprocal of \(\frac{\sqrt{3}}{2}\):
\[ B = 0.50 \cdot \frac{2}{\sqrt{3}} = \frac{1}{\sqrt{3}} \text{ oersted} \]

5. **Final result**: Therefore, the total magnetic field at that place is:
\[ B = \frac{1}{\sqrt{3}} \text{ oersted} \]