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A magnetic needle has a magnetic moment ...

A magnetic needle has a magnetic moment `5xx 10^(-2) "Am"^(2)`. If the moment of inertia of a magnet about an axis passing through the centre and perpendicular to the length of a magnet is `1.0 xx 10^(-7)"kgm"^(2)` then calculate the magnitude of the magnetic field which sets the magnet into oscillation at a frequency of 2 Hz.

Text Solution

Verified by Experts

Given : `|vecm| = 5xx10^(-2) "Am"^(2), I = 1.0 xx 10^(-7) "kgm"^(2)`
f = 2Hz so that`T = (1)/(f) = 0.5 s`
We know that , ` T = 2pi sqrt((I)/(mB))`
i.e., `" " B = (4pi^(2)I)/(mT^(2))= (4xx(3.14)^(2)xx10^(-7))/(5xx10^(-2)xx0.25) = 31.55xx10^(-5)`T
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