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

Explanation

Here,
Magnetic moment, `M = 6.7 xx 10 ^(-2) A - m ^(2)`
Moment of inertia, `l = 7.5 xx 10 ^(-6) kg - m ^(2)`
Time taken for one oscillation, `fT = ( 6.7)/(10) = 0. 67 s`
Magnetic field,
`B = ( 4 pi ^(2) l )/( MT ^(2)) = ( 4 xx ( 3.14) ^(2) xx 7.5 xx 10 ^(-6))/( 6.7 xx 10 ^(-2) xx (0. 67) ^(2))`
`therefore B = 9.83 xx 10 ^(-3) T`