A dip needle vibrates in the vertical plane perpendicular to...

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be $2 \mathrm{sec}$. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2 \mathrm{sec}$. Then the angle of dip is (a) $0^{\circ}$ (b) $30^{\circ}$ (c) $45^{\circ}$ (d) $90^{\circ}$

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be $2 \mathrm{sec}$. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2 \mathrm{sec}$. Then the angle of dip is
(a) $0^{\circ}$
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $90^{\circ}$

Key Concepts

Magnetic Dip (Inclination Angle)

This concept refers to the angle that the Earth’s magnetic field makes with the horizontal plane. It is a fundamental property of the Earth’s magnetism, determining how the field is distributed among its horizontal and vertical components. The dip angle is crucial for understanding the behavior of magnetic instruments, such as needles, when they oscillate in different planes, since the restoring torques depend on the orientation of these field components.

Simple Harmonic Motion in Magnetic Fields

When a magnetic needle is displaced from equilibrium, it experiences a restoring torque that can lead to oscillatory motion, which, under small angle approximations, is described as simple harmonic motion (SHM). The period of oscillation in SHM is determined by the moment of inertia of the needle and the effective torque provided by the magnetic field. Analyzing the time period in different planes allows inference of the magnetic field’s components influencing the motion.

Magnetic Field Components

The Earth's magnetic field can be decomposed into horizontal and vertical components. These components are essential in the study of magnetic oscillations because they exert different restoring torques on a vibrating needle depending on the plane of oscillation. The relationship between these components, and consequently the dip angle, influences the period of oscillation observed in both the horizontal and vertical planes.

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