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A bar magnet is oscillating in the Earth's magnetic field with periodic time T. If a similar magnet with the same mass and volume has a magnetic dipole moment which is 4 times that of this magnet, then its periodic time will be ______.

Asked in GSEB Board July 2015 · Dipole in a uniform field

Answer: (1) T/2

Step-by-step solution

Given: same mass and volume, so the same moment of inertia I; same place, so the same horizontal field B_H; the new moment is m'=4m.

Idea: a magnet oscillating in a horizontal field is an angular harmonic oscillator of period T=2π√I/(mB_H), in which mB_H plays the part of the stiffness.

Only m changes, so T∝1/(√m).

(T')/T=√m/(m')=√1/4=1/2.

T'=T/2: the stronger magnet is pulled back harder and oscillates twice as fast.

Why the other options are wrong

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