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A charged particle near a current-carrying wire does not experience a magnetic force when its velocity is equal to $0$. So why does a compass needle kept near a current carrying wire experience a force when the compass needle is at rest?

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A compass needle is magnetized and will experience a force or torque when placed in an external magnetic field such as one produced by a nearby current carrying wire. The compass needle is said to have a "magnetic moment" which measures how magnetized it is, and therefore how strongly it responds to external magnetic fields. Sometimes, magnetic materials like the compass needle are modeled by loops of current, similar to a solenoid. Since the current is moving charges, $v \ne 0$, they will experience the forces which produces the movement of the compass needle.

I hope this helps.

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  • $\begingroup$ But this means not all compass needles are modeled by loops of current , so what could be the possible reason of deflection of such needles of compass in the vicinity of current carrying wire? $\endgroup$ Oct 16, 2020 at 19:45

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