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A magnetic needle has magnetic moment M=...

A magnetic needle has magnetic moment `M=6.7 xx 10^(-2) A.m^(2)` and moment of inertia `I = 7.5 xx 10^(-6)kg.mn^(2).` It performs 10 complete oscillations in 10 s. Find the magnitude of the magnetic field.

Text Solution

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Given, magnetic moment,
`M = 6.7 xx 10 ^(-2) A - m ^(2)`
Moment of intrtia, `l = 7. 5 xx 10 ^(-6) kg - m ^(2)`
Time taken for 1 oscillatio, `T = (10)/(10) = 1s`
Magnitude of the magnetic field,
`B = ( 4 pi ^(2) l )/( MT ^(2)) = ( 4 xx (31.4) ^(2) xx 7.5 xx 10 ^(-6))/( 67 xx 10 ^(-2) xx (1) ^(2))`
`therefore B = 4.4 xx 10 ^(-3) T`
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