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I understand that the strength of a magnetic field decreases as you get further away from the source of the field.

However, whats the strength of the field within a magnet? Is there a field in a magnet?

Like if I have a bar magnet, is there a $B$-field in that metal chunk?

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Yes, there must be. The solenoidal law tells us that the normal component of the B-field must be continuous across any interface. There are no sources or sinks of B-field. Therefore the lines of magnetic field are continuous through your bar magnet - they come in through one end (very roughly speaking) and out through the other.

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