A magnet makes 40 oscillations per minute at a place having a magnetic field intensity of $0.1 \times 10^{−5} T$. At another place, it takes 2.5 sec to complete one vibration. The value of earth's horizontal field at that place :
A) $0.25 \times {10^{ - 6}}T$
B) $0.36 \times {10^{ - 6}}T$
C) $0.66 \times {10^{ - 6}}T$
D) $1.2 \times {10^{ - 6}}T$

Hint: The magnetic field intensity is also called magnetic intensity or magnetic field strength. The time taken by the particle to complete one oscillation is called the period of oscillation. It is denoted by the letter T.

Complete step by step solution:
No of oscillations made by the magnet = 40
The magnetic field intensity, ${B_{H1}} = 0.1 \times {10^{ - 5}}T$
The value of the earth’s horizontal field, ${B_{H_2}} = ?$
We know that the period of oscillation is given by the formula,
$T = 2\pi \sqrt {\dfrac{1}{{m{B_H}}}} $
From the above formula, we can say that \[T \propto \dfrac{1}{{\sqrt {{B_H}} }}\]
$ \Rightarrow \dfrac{{{T_1}}}{{{T_2}}} = \sqrt {\dfrac{{{B_{H_2}}}}{{{B_{H_1}}}}} $
Here ${T_1} = \dfrac{{40}}{{60}},{T_2} = 2.5,{B_{H_1}} = 0.1 \times {10^{ - 5}}$
$ \Rightarrow \dfrac{{\dfrac{{40}}{{60}}}}{{2.5}} = \sqrt {\dfrac{{{B_{H_2}}}}{{0.1 \times {{10}^{ - 5}}}}} $
$ \Rightarrow {{\rm B}_{H_2}} = 0.36 \times {10^{ - 6}}T$
Thus the value of the earth’s horizontal field, ${{\rm B}_{H_2}} = 0.36 \times {10^{ - 6}}T$

Hence the correct option is B.

Additional Information:
1. Magnetization is also called magnetic polarization and is the vector field that represents the density of the induced magnetic dipole moments in a material. It depends on the size of the dipole moments of the atoms in a given substance and also the degree to which these dipole moments are aligned to each other.
2. Electromagnetic waves are defined as the waves that are propagated by the simultaneous periodic variations of the electric field and the magnetic field intensity.

Note: 1. The magnetic field strength or the magnetic field intensity is defined as the ratio of the magnetomotive force that is needed to create flux density per unit length of a given material.
2. The period of oscillation is proportional to the moment of inertia of the magnet.
3. The magnetic field of Earth is produced deep down the earth’s core. An electric current is generated by the Earth core when the flow of liquid iron produces magnetic fields.