Question

At a certain place, the angle of dip is $30°$ and the horizontal component of the earth's magnetic field is $0.50\mathrm{oersted}$. The earth's total magnetic field (in oersted) is

• A. $\sqrt{3}$
• B. 1
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C

$\frac{1}{\sqrt{3}}$

Step 1: Given parameters

The angle of dip, $\mathrm{\theta }=30°$

The horizontal component of the earth's magnetic field, $\mathrm{H}=0.50\mathrm{oersted}$

Step 2: To find

We have to find the earth's total magnetic field (in oersted).

Step 3: Calculation

We know the formula,

Magnetic field, $\mathrm{B}=\frac{\mathrm{H}}{\mathrm{Cos\theta }}$

Here,

H is the horizontal component.

$\mathrm{\theta }$ is the angle of dip.

By substituting the given values in the formula, we get

$$\begin{gathered} \mathrm{B}=\frac{0.50}{\mathrm{Cos}30°} \\ =\frac{0.50\times 2}{\sqrt{3}} \\ =\frac{1}{\sqrt{3}} \end{gathered}$$

Therefore, option C is the correct choice.