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The axial magnetic field at a distance from a magnet falls-off as l/d3 (note: 3 is the power of d, meaning d cube, it's not multiplying with d) where d is the distance to the magnet. A small, strong, permanent magnet generates a magnetic field that is measured by a small probe placed on its axis. It is desired to use the strength of the measured field to find the position of the (slowly moving) probe. What is the minimum number of bits of an analogue to digital converter in order to measure position to a precision of l mm over a distance range from 10cm to 20cm. Give some practical considerations for improving the accuracy of measurement.
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This solution is provided in 197 words. It discusses how bits relates to accuracy and how improvement to accuracy can be made.
Because measurement is to be done between 10 cm and 20 cm, i.e., 1000 mm to 2000 mm with accuracy of 1 mm. In other words 2000-1000 = 1000 is to be measured with accuracy of 1, and because 2^10 = 1024, therefore, 10 bits will be sufficient for this accuracy. ...
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