Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It:

will become rigid showing no movement

will stay in any position

will stay in north-south direction only

will stay in east-west direction only

Earth's Magnetic Field at Poles: At the geomagnetic poles, the magnetic field lines of the Earth are directed vertically (perpendicular to the surface). This means the angle of dip (or inclination, $I$ or $\delta$ ) is $90^\circ$ .
Horizontal Component: The horizontal component of the Earth's magnetic field ( $H_E$ ) is related to the total magnetic field ( $B$ ) and the angle of dip by the equation: $H_E = B \cos \delta$ At the poles, since $\delta = 90^\circ$ , $H_E = B \cos 90^\circ = 0$ . Thus, the horizontal component of the Earth's magnetic field is zero.
Effect on Compass: A compass needle is designed to move in a horizontal plane and aligns itself with the horizontal component of the magnetic field. The torque ( $\tau$ ) exerted on the needle is given by $\tau = m H_E \sin \theta$ . Since $H_E = 0$ , the torque is zero regardless of the orientation ( $\theta$ ) of the needle.
Conclusion: With no restoring torque to align it to a specific direction, the compass needle is in neutral equilibrium and will remain in any position in which it is placed.

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