Question

The relation between ${{\text{B}}_{\text{ }\\!\\!\upsilon\\!\\!\text{ }}}\text{, }{{\text{B}}_{\text{h}}}$and $\text{B}$is ______.

A.)$B=\sqrt{{{B}_{h}}^{2}+{{B}_{\upsilon }}^{2}}$
B.)$B={{B}_{h}}\cdot {{B}_{\upsilon }}$
C.)$B=\dfrac{{{B}_{h}}}{{{B}_{\upsilon }}}$
D.)$B=\dfrac{{{B}_{\upsilon }}}{{{B}_{h}}}$

Answer 1

Hint: ${{B}_{v}}$and${{B}_{h}}$are the vertical and horizontal components of earth’s magnetic field respectively. $B$is the resultant magnetic field of Earth. Both vertical and horizontal components are associated with the angle of dip.

Complete step by step answer:
Earth’s magnetic field extends from the Earth’s interior out into the space and there it interacts with the solar wind. The magnetic field of Earth is caused by the currents of electricity which are flowing in the molten state. The intensity of the magnetic field is greatest near the magnetic poles where it is actually vertical. The intensity of the field is weakest near the equator where it is horizontal.

Angle of dip, which is also called dip angle, is defined as the angle which Earth’s magnetic field lines make with horizontal. Its value varies from point to point because of the movement of Earth’s magnetic field lines. The value of dip angle is said to be positive when the magnetic field points downwards and when magnetic field lines point upwards, dip angle becomes negative. The angle of dip at the equator is zero because at the equator, magnetic field lines are aligned perfectly horizontally.

Horizontal component of Earth’s magnetic field ${{B}_{h}}=B\cos \delta$
Vertical component of Earth’s magnetic field ${{B}_{v}}=B\sin \delta$
Resultant magnitude of two vectors,${{B}^{2}}={{B}_{h}}^{2}+{{B}_{v}}^{2}$
We get, $B=\sqrt{{{B}_{h}}^{2}+{{B}_{v}}^{2}}$

Hence, the correct option is A.

Note:
The three components which are responsible for deciding the magnitude and direction of Earth’s magnetic field are: Magnetic declination, Angle of dip, and Horizontal component of Earth’s magnetic field.