Q. 19

# A bar magnet of magnetic moment m and moment of inertia I (about center, perpendicular to length) is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the mid-point, perpendicular to length, in a magnetic field B. What would be the similar period T’ for each piece?

Answer :

Time period

Where, I = Moment of inertia of bar magnet

M = mass of the magnet

B = Magnetic Field

Bar magnet is oscillating in Uniform Magnetic Field

Moment of Inertia

Initial time period

When the bar magnet is cut into two equal pieces each of mass () and length ()

Hence

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PREVIOUSSuppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of (i) electric dipole p in an electrostatic field E and (ii) magnetic dipole m in a magnetic field B. Write down a set of conditions on E, B, p, m so that the two motions are verified to be identical. (Assume identical initial conditions.)NEXTUse (i) the Ampere’s law for H and (ii) continuity of lines of B, to conclude that inside a bar magnet, (a) lines of H run from the N pole to S pole, while (b) lines of B must run from the S pole to N pole.

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