A thin rectangular bar magnet is successively broken into smaller pieces
MATHEMATICS · Multi-part · ISC · Physics · Magnetic Effects of Current and Magnetism · Magnetic field and dipoles
Problem
A thin rectangular bar magnet is successively broken into smaller pieces, each break being a clean transverse fracture perpendicular to the original long axis.
• After the first break the original magnet becomes 2 equal pieces.
• After the second break each of those pieces is broken again in the same manner, giving 4 equal pieces.
• The process continues so that after n breaks, N(n) equal-size magnet pieces are produced.
(a) For the original unbroken magnet, state the number of exposed magnetic pole faces (count only the surfaces at which a North or South pole is present).
(b) After one break (n=1), determine N(1) and the total number of exposed pole faces.
(c) Derive a general expression for the total number of exposed pole faces after n breaks, in terms of n.
(d) Evaluate your expression for n=4, and describe how the arrangement of poles on the collection of pieces would appear if they were laid end-to-end in their original order with small gaps between adjacent pieces.
(e) If all N(n) pieces are reassembled without gaps into their original configuration, explain why the external magnetic field far from the reassembled bar is essentially indistinguishable from that of the original single magnet.