Question

At two places A and B using a vibration magnetometer, a magnet vibrates in a horizontal plane and its respective periodic time are 2 sec and 3 sec and at these places the earth's horizontal components are HA and HB respectively. Then the ratio between HA and HB will be
A. 9:4
B. 3:2
C. 4:9
D. 2:3

Answer 1

Hint: Before starting this question, we should know about magnetic dipole moments. A magnetic dipole is made up of magnetic north and south poles that are close together. Current times area or energy divided by magnetic flux density are the dimensions of magnetic dipole moments. Ampere-square metre is the unit for dipole moment in metre-kilogram-second-ampere.

Formula used:
 The time period for oscillation can be calculated as:-
$T=2π\sqrt{\dfrac{I}{MB}}$ ,where I is the moment of inertia, M is the magnetic moment and B is the magnetic field.

Complete step by step solution:
Vibration magnetometer is a device that works on the principle that if in the uniform magnetic field a freely suspended magnet is disturbed from its equilibrium position and starts vibrating or oscillating from its mean position. It is used to compare magnetic moment and magnetic field.

According to the question,
$T=2\pi \sqrt{\dfrac{i}{MH}}$
$\Rightarrow T\propto \dfrac{1}{\sqrt{H}}$
$\Rightarrow \dfrac{{{T}_{A}}}{{{T}_{B}}}=\sqrt{\dfrac{{{H}_{B}}}{{{H}_{A}}}}$
$\Rightarrow \dfrac{{{H}_{A}}}{{{H}_{B}}}={{\left( \dfrac{{{T}_{B}}}{{{T}_{A}}} \right)}^{2}}={{\left( \dfrac{3}{2} \right)}^{2}}=\dfrac{9}{4}$

Hence, option A is correct.

Note: Dynamo effect is one theory that explains the cause of earth magnetism. There are certain metallic fluids present at the outer core as well as inner core due to which magnetic field lines are caused. Molten iron and solidified elements are the components of outer core and inner core respectively. While solving the questions related to earth magnetism or any numerical one should analyse what all is the given data and then proceed with the best fit formula in order to find the most accurate and correct answer.