Question

In the magnetic meridian of a place, the horizontal component of the earth's magnetic field is 0.26, and the dip angle is ${{60}^{\circ }}$. What is the magnetic field of the earth at this location?

Answer 1

Hint: Earth's magnetic field, also known as the geomagnetic field, is a field that extends from the earth's interior out into space. The horizontal components stretch from the beginning of the vector to the end of its x-coordinate. The vertical component stretches from the x-axis to the vertical point on the vector. We should be considering the horizontal and vertical components of the earth's crust to find the magnetic field of the earth.

Complete step-by-step answer:
To solve this question, let us consider the earth's magnetic field as ${{\text{B}}_{\text{e}}}$. Let us also consider the horizontal and vertical components of the earth's magnetic field as ${{\text{H}}_{\text{e}}}$ and ${{\text{H}}_{\text{v}}}$ respectively. The dip angle being ${{60}^{\circ }}$ and the horizontal component of earth's magnetic field being 0.26, we can derive the magnetic field of the earth with the following mathematical equations.
$\begin{aligned} & \text{cos }\\!\\!\theta\\!\\!\text{ = }\dfrac{{{\text{H}}_{\text{e}}}}{{{\text{B}}_{\text{e}}}} \\\ & \therefore \text{ cos }{{60}^{\circ }}\text{ = }\dfrac{0.26\text{ }\times \text{ 1}{{\text{0}}^{-4}}}{{{\text{B}}_{\text{e}}}} \\\ & \Rightarrow \text{ }{{\text{B}}_{\text{e}}}\text{ = }\dfrac{0.26\text{ }\times \text{ 1}{{\text{0}}^{-4}}}{\dfrac{1}{2}}\text{ = 0}\text{.52 }\times \text{ 1}{{\text{0}}^{-4}}\text{ T = 0}\text{.52 G} \\\ \end{aligned}$
Where T stands for tesla and G stands for gauss.
With the given equations, we can find out that the magnetic field of the earth at the given location is 0.52G.
Therefore, the correct answer is 0.52G.

Additional Information:
Convection currents are caused by heat escaping from the core, which is a natural process. The magnetic field of the earth is generated by electric current due to the motion of convection currents of a mixture of molten iron and Nickel in the earth's outer core.

Note: The earth’s magnetic field is also known as the geomagnetic field. It extends to tens of thousands of kilometers in space. While the North and the South magnetic poles are usually located near the geographic poles, this slowly and continuously moves over geological time scales but slowly for ordinary compasses to keep track and maintain usefulness for navigation.