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Measure surface

If I have a neomagnet with a Br of 12,300 gauss, can I measure 12,300 gauss on its surface?

No. Br-value is measured in a closed circuit. A closed circuit magnet is not very useful. In practice, you will measure a field that is less than 12,300 gauss near the surface of the magnet. The actual measurement will depend on whether the magnet is connected to steel, how far from the surface you are taking the measurement, and the size of the magnet (assuming the measurement is taken at room temperature). A neodymium magnet that is 1" in diameter and ¼" long measures about 2,500 gauss when it is 1/16" from the surface and 2,200 gauss when it is 1/8" from the surface.