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Magnetism and Matter
Oscillations of a Magnet in a Magnetic Field
1 question, with its answer.
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Two bar magnets having same geometry with magnetic moments M and 2M, are firstly placed in such a way that their similar poles are same side then its time period of oscillation is $T_1$. Now the polarity of one of the magnets is reversed then time period of oscillation is $T_2$, then : -Time period of a magnet oscillating in a uniform field: $T = 2\pi\sqrt{\dfrac{I}{MB}}$, so $T \propto \dfrac{1}{\sqrt{M}}$ (the moment of inertia I is the same in both cases).
Case I (similar poles together): $M_1 = 2M + M = 3M$
Case II (one reversed): $M_2 = 2M - M = M$
$\dfrac{T_1}{T_2} = \sqrt{\dfrac{M_2}{M_1}} = \sqrt{\dfrac{M}{3M}} = \dfrac{1}{\sqrt{3}} \Rightarrow T_2 = \sqrt{3}T_1$
So $T_1 \lt T_2$.
That is every question in Oscillations of a Magnet in a Magnetic Field.
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