A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are mutually perpendicular and bisect each other. The time period of the combination is 4 s . If

Question

A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are mutually perpendicular and bisect each other. The time period of the combination is 4 s . If one of the magnets is removed, then the time period of other one will be

TestHub · Accepted Answer

As magnets are perpendicular to each other, the resultant magnetic moment

$M' = \sqrt{M^{2} + M^{2}} = \sqrt{2} M$

$∴ T_{1} = 2 π \sqrt{\frac{2 I}{(\sqrt{2} M) H}}$

In the second case, $T_{2} = 2 π \sqrt{\frac{I}{MH}}$

$\frac{T_{2}}{T_{1}} = \frac{1}{{(2)}^{1 / 4}}$

$∴ T_{2} = \frac{4}{{(2)}^{1 / 4}} = 3.36 s$

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