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Have you cut a magnet?

I bought a small handful of motor & dummy trucks off da bay the other day, all die cast PW stuff that fits 2032, 2023, etc. One of the motor trucks is missing both magnets. Now, I can buy two purpose-made Alnico magnets from a parts supplier for $10 total, or for about the same $$, I can buy a small gob of neodymium magnets (likely much stronger than the original Alnico magnets) that are entirely too long. So here's the question(s):

1. If you cut a bar magnet (let's just say in half), do the two new pieces now take on the North/South properties of the original magnet, i.e. do both pieces have proper poles?

2. Are they each half as strong as the original?

3. If yes, can you now stack those two pieces, North on North and South on South, and get a single magnet with the same strength as the original? I would imagine stacking two opposing pole pieces would be easy, but stacking two same-pole pieces would be a bit like herding cats - dang near impossible, even with JB Weld!

They are on order for $12, so it's cheap enough to just experiment with, but I'm curious if anyone else has re-Magnetractioned a truck in this way?

Do you suppose that if this worked really, really well that you could now have a truck with so much magnetraction it wouldn't even want to roll down the track?

Aaaaah, Sunday mornings are great times for pondering....

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