A small magnetic needle performs small oscillations about an axis perpendicular to the magnetic induction vector. On changing the magnetic induction the neddle's oscillation period decreases `eta=5.0` times. How much and in what way was the magnetic induction changed ? The oscillation damping is assumed to be negligible.

Explanation

In a magnetic field of indction `B` the couple on the magnet is `-MB sin theta=- MB theta ` equating this to `I ddot(theta)` we get
`I ddot (theta)+MBtheta=0`
or `omega^(2)=(MB) /(I) ` or `T=2pi sqrt((I)/(mg))`
Given `T_(2)=T_(1)//eta`
`sqrt((1)/(B_(2)))=sqrt((1)/(B_(1))).(1)/(eta)` or `(1)/(B_(2))=(1)/(B_(1)).(1)/(eta_(2))`
or `B_(2)=eta^(2)B_(1)`
The induction of the field increased `eta^(2)` times.