Write the expression for the time period of oscillation of a small compass needle in a uniform magnetic field and explain the terms. In this case, if the magnitude of the magnetic field is reduced to `1//4^(th)` , how does the time period change ?

Explanation

Time period of oscillation of a small compass needle in a uniform magnetic field is .
`T=2pisqrt(I/(piB))`
Where T = time period , I=moment of inertia of the dipole
B=magnetic filed , m=magnetic moment .
If the magnetic field B is reduced to `1//4^(th)` i.e., B becoming `B/4`, Time period `T=2pisqrt(I/(mB//4))=2pisqrt((4I)/(mB))=2pixx2sqrt(I/(mB))`
`T=2xx2pisqrt(I/(mB))`
When B becomes `B//4` , T gets doubled.