Can You Create a Circular Magnet with Circular Magnetisation?

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DrZoidberg
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What happens when you try to create a ring shaped magnet with a circular magnetisation.
e.g. you take an unmagnetised steel ring, wind some copper wire around it, turn on the current for a few seconds and then remove the wire. Afterwards there should be a circular magnetic field inside the ring right? Will there be any field outside?
 
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Try googling "magnetic keepers".