Time period of a thin bar magnet of vibration magnetometer is given by
T=2π√‌ where,
I is moment of inertia of a bar magnet of mass
mb, length
l about an axis passing through its centre and perpendicular to its length,C
I=‌ M is magnetic moment of bar magnet, i.e.
M=m×l, where
m is magnetic strength of bar magnet and
H is the uniform magnetic field in which the magnet is oscillating.
Case I When magnet is cut parallel to its length
I′‌‌=‌⋅‌=‌=‌ ‌ and ‌M′‌‌=‌×l=‌ ∴ Time period of each part, when bar magnet is cut parallel to its length is
T′=2π√‌=2π√‌ ⇒T′=2π√‌=T Case II When magnet is cut perpendicular to its length.
I′′=‌⋅‌= and
M′′=m×‌=‌ ∴ Time period of each part, when bar magnet is cut perpendicular to its length is
T′′‌‌=2π√‌=2π√‌ T′′‌‌=2π√‌=‌×2π√‌ ⇒T′′‌‌=‌