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A small compass needle of magnetic momen...

A small compass needle of magnetic moment M is free to turn about an axis perpendicular to the direction of uniform magnetic field B. The moment of inertia of the needle about the axis is I. The needle is slightly displaced from its stable position and then released. Prove that it executes simple harmonic motion. Hence deduce the expression for its time period.

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To solve the problem, we need to show that the small compass needle executes simple harmonic motion (SHM) when slightly displaced from its stable position in a uniform magnetic field. We will also derive the expression for its time period. ### Step-by-Step Solution: 1. **Understanding the System**: - We have a small compass needle with a magnetic moment \( M \) that can rotate about an axis perpendicular to the direction of a uniform magnetic field \( B \). - The moment of inertia of the needle about this axis is \( I \). ...
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