Question

Review. (c) Assume the dipole is a compass needle-a light bar magnet-with a magnetic moment of magnitude μ . It has moment of inertia I about its center, where it is mounted on a frictionless, vertical axle, and it is placed in a horizontal magnetic field of magnitude B. Determine its frequency of oscillation.

Answer 1

The frequency of oscillation is $\frac{1}{2\pi } \sqrt{\frac{\mu B}{I} }$.

What is a magnetic moment?

The magnetic moment is the magnetism of a magnet or other item that creates a magnetic field, as well as its orientation and strength. Electromagnets, permanent magnets, elementary particles like electrons, different compounds, and a variety of celestial objects are examples of things that have magnetic moments (such as many planets, some moons, stars, etc). The phrase "magnetic moment" typically refers to a system's magnetic dipole moment, which can be represented by an analogous magnetic dipole, which has a magnetic north and south pole that are barely separated from one another. For sufficiently small magnets or at sufficiently wide distances, the magnetic dipole component is adequate. For extended objects, additional terms may be required in addition to the dipole moment, such as the magnetic quadrupole moment.

$T = \frac{ Id^{2}\theta }{dt^{2} }$

$-\mu B\theta=\frac{ Id^{2}\theta }{dt^{2} }$

$\frac{d^{2}\theta }{dt^{2} } = -(\frac{\mu BI}{\theta} )$

By Comparing the above equation with the SHM equation

$\frac{d^2 \theta} {dt^{2} } = -\omega^{2} \theta$

$\omega^{2} =\frac{ \mu B}{I}$

Frequency = $\frac{\mu}{2\pi }$

=$\frac{\sqrt{\frac{\mu B}{I} } }{2\pi}$

=$\frac{1}{2\pi } \sqrt{\frac{\mu B}{I} }$

To learn more about a magnetic moment, visit:

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