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Hall sensors is used to detect the magnetic flux leakage. It means the that sensor moves along a surface of a plate and detect a magnetic flux leakage which is an alternating magnetic field. What is the effect of the velocity of the Hall sensor on received signal? What is the difference between two received signals when Hall sensor does not move and when it moves?

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Whew.
Hall effect sensing does not require, or prohibit, the sensor or sensed magnetic field, be in motion. Hall effect valid for stationary and unchanging magnetic fields as well as rapidly changing field - up to the limits in speed imposed by device characteristics.

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