A magnetic needle placed in uniform magnetic field has magnetic moment `6.7 xx 10^(-2) "Am"^(2)`, and moment of inertia of `15 xx 10^(-6)` k `m^(2)`. It performs 10 complete oscillations in 6.70 s. What is the magnitude of the magnetic field ?

Explanation

Dipole moment ` = 6.7 xx 10^(-2) "Am"^(2)`
Moment of inertia `I= 15 xx 10^(-6) "Kg m"^2`
Periodic time T `= ("time")/("No. of oscillations")`
`- (6.7)/(10) -0.67` s
The period of magnetic needle placed in uniform magnetic field,
`T= 2pi sqrt((I)/( mB))`
`therefore T^(2) = (4 pi^(2) I)/( mB)`
`therefore B= (4pi^(2) I)/( mT^(2) )`
`= (4 xx (3.14)^(2) xx 15 xx 10^(-6) )/( 6.7 xx 10^(-2) xx (0.67)^(2) )`
`= 196.69 xx 10^(-4)`
`therefore B ~~ 0.02` T