A bar magnet has a magnetic moment equal to 5 ×10^-5 Wb-m . It is suspended in a magnetic field

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A bar magnet has a magnetic moment equal to 5 ×10^-5 Wb-m ....

A bar magnet has a magnetic moment equal to $5 \times 10^{-5} \mathrm{~Wb}-\mathrm{m} .$ It is suspended in a magnetic field which has a magnetic induetion $B$ equal to $8 \pi \times 10^{-4} \mathrm{~T}$. The magnet vibrates with a period of vibration equal to 15 s. The moment of inertia of magnet is (a) $4.54 \times 10^{4} \mathrm{~kg}-\mathrm{m}^{2}$ (b) $4.54 \times 10^{-5} \mathrm{~kg}-\mathrm{m}^{2}$ (c) $4.54 \times 10^{-4} \mathrm{~kg}-\mathrm{m}^{2}$ (d) $4.54 \times 10^{5} \mathrm{~kg}-\mathrm{m}^{2}$

A bar magnet has a magnetic moment equal to $5 \times 10^{-5} \mathrm{~Wb}-\mathrm{m} .$ It is suspended in a magnetic field which has a magnetic induetion $B$ equal to $8 \pi \times 10^{-4} \mathrm{~T}$. The magnet vibrates with a period of vibration equal to 15 s. The moment of inertia of magnet is
(a) $4.54 \times 10^{4} \mathrm{~kg}-\mathrm{m}^{2}$
(b) $4.54 \times 10^{-5} \mathrm{~kg}-\mathrm{m}^{2}$
(c) $4.54 \times 10^{-4} \mathrm{~kg}-\mathrm{m}^{2}$
(d) $4.54 \times 10^{5} \mathrm{~kg}-\mathrm{m}^{2}$

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Key Concepts

Magnetic Dipole Moment

This is a vector quantity characterizing the strength and direction of a magnet or current loop. It determines how the dipole interacts with external magnetic fields, experiencing torques that cause alignment with the field.

Torque on a Magnetic Dipole

When placed in a magnetic field, a magnetic dipole experiences a torque that causes it to oscillate about an equilibrium orientation. The magnitude of this torque is the product of the magnetic dipole moment, the magnetic field strength, and the sine of the angle between them.

Rotational Simple Harmonic Motion

The oscillatory motion of a magnetic dipole in a magnetic field can be modeled as simple harmonic motion. The period of these oscillations depends on both the restoring torque provided by the magnetic field and the dipole's moment of inertia.

Moment of Inertia

This is a measure of an object's resistance to changes in its rotational motion. In the context of oscillatory systems, it appears in the equation for the period of rotational oscillations, linking the dynamics of rotational motion with the characteristics of the system.

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