A bar magnet of magnetic moment $M$ and pole strength ' $m$ ' is cut into $100$ similar pieces parallel to the magnetic axis and each piece is cut into $200$ similar pieces perpendicular to the magnetic axis. Find magnetic moment similar pieces perpendicular to the magnetic axis. Find magnetic moment and pole strength of smallest piece.

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Solution

We know that magnetic moment $M = m l$ . When magnet cur parallel to magnetic axis their pole strength is divided. New pole strength is $M^{'} = \frac{m}{100}$ after $100$ divisions.
When magnet is cut perpendicular to magnetic axis then pole strength is constant but strength is reduced
New length $l^{'} = \frac{l}{200}$
New magnetic moment is $M^{'} = \frac{m}{100} \times \frac{l}{200} = \frac{M}{20000}$

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