Question

The value of the horizontal component of earth’s magnetic field at a place is $$0.35 \times {10^{ - 4}}\,T$$ . If the angle of dip is ${60^ \circ }$ , the value of vertical component of earth’s magnetic field is nearly:
A) $$0.1 \times {10^{ - 4}}\,T$$
B) $$0.2 \times {10^{ - 4}}\,T$$
C) $$0.4 \times {10^{ - 4}}\,T$$
D) $$0.61 \times {10^{ - 4}}\,T$$

Answer 1

Hint: Horizontal component of Earth’s magnetic field is given. The angle of dip is given. The ratio of Earth’s vertical magnetic field and horizontal magnetic field is equal to the tangent of angle of dip.

Complete step by step solution:
The magnetic field is divided into horizontal and vertical components. The Earth's magnetic field, which effectively extends to several tens of thousands of kilometres into space, forms the Earth's magnetosphere.
The horizontal component of Earth’s magnetic field is given as:
$${B_H} = 0.35 \times {10^{ - 4}}\,T$$
And the angle of dip $\delta = {60^ \circ }$
We know that the ratio of Earth's horizontal magnetic field to the Earth’s vertical magnetic field is equal to the tangent of the angle of dip.
Therefore, we have:
$\dfrac{{{B_V}}}{{{B_H}}} = \tan \delta $
$ \Rightarrow {B_V} = {B_H}\tan \delta $
Substituting the given values, we can have:
${B_V} = 0.35 \times {10^{ - 4}}\,T \times \tan {60^ \circ }$
$ \Rightarrow {B_V} = 0.35 \times {10^{ - 4}}\,T \times \sqrt 3 $
$ \Rightarrow {B_V} = 0.6062 \times {10^{ - 4}}\,T$
Therefore, the value of the vertical component magnetic field is $0.61 \times {10^{ - 4}}\,T.$

Option D is the correct option.

Additional information: The Earth's magnetic field is produced due to the fluid in the outer core by a self-exciting dynamo process. The magnetic field is generated due to the electrical currents flowing in the slowly moving molten. The magnetic field of Earth is losing on a daily basis. In the last two centuries, Earth has lost nearly $9\% $ of its magnetic field. The direction of the magnetic poles of the Earth is changing and sometimes it also gets reserved.

Note: The component of the Earth’s magnetic field can be spit into the horizontal and vertical components. Remember, that the ratio of vertical component of the Earth’s magnetic field to the horizontal component of Earth’s magnetic field is equal to the tangent of the angle of dip.