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A bar magnet having pole strength qₘ and magnetic moment m is divided into two equal parts along its length. The new pole strength is _________ and the magnetic moment is __________ respectively.

Asked in GUJCET 2023 · Magnetic moment of magnets and loops

• (1) qₘ and m/2
• (2) (qₘ)/2 and m
• (3) (qₘ)/2 and m/2
• (4) qₘ and m

Step-by-step solution

Why the other options are wrong

• (1) This is what a cut across the magnet gives: there the pole faces are untouched, so the pole strength stays and the length halves. A cut along the length halves the pole faces instead.
• (2) Halves the pole strength but keeps the moment. Since m=qₘ×2l and a lengthwise cut leaves the length 2l alone, halving qₘ must halve m with it.
• (4) If nothing changed, one magnet would become two magnets each as strong as the original and the total moment would double. The magnetisation and the total volume are unchanged, so the moment has to divide between the halves.

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