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Let the magnetic moment of a bar magnet be vec(p_(m)) whose mangetic length is d = 2l and pole strenght is q_(m). Compute the magnetic moment of the bar magnet when it is cut into two pieces. (a) along its length(b) perpendicular to its length |
Answer» Solution :A bar magnet CUT into two pieces along its length :  When the bar is cut along the axis into two pieces. New magnetic pole STRENGTH is `q_(m)^(.) = (q_(m))/(2)` but magnetic length does not change . So. The magnetic moment is `p_(m)^(.) = q_(m)^(.)` 2l `p_(m)^(.) = (q_(m))/(2) 2l = (1)/(2) (q_(m) 2l) = (1)/(2) p_(m)` In vector NOTATION. `vec(P.)m = (1)/(2) vec(P)`m (b) a bar magnet cut into two pieces perpendicular to the `a xx` is : When the bar magnet is cut perpendicular to the axis into two pieces, magnetic pole strength will not change but magnetic length will be halved. So the magnetic moment is `p._(m) = q_(m) xx (1)/(2) (2l) = (1)/(2) (q_(m) . 2l) = (1)/(2) p_(m)` `vec(p._(m)) = (1)/(2) vec(P_(m))` 
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