Can a Magnetic Field Really Induce a Potential Difference in the Hall Effect?

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The idea behind the Hall effect is according to my book that the magnetic field induces a charge distribution such that there is more positive charge on one side and more negative on the other. This induces a potential difference. But the question is: Is this the correct way to view it? I mean after all the charges are never stationary and even so, how is it possible for a magnetic field, which can do no work, to establish a potential difference?
 
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Magnetic Field is not doing any work, it merely changes the direction of motion of moving electrons and holes. Just as a curved slide > _/ would throw any object upwards if the object come running towards it, without ever doing any work(by slide), you would find the object's potential energy increased(in gravity). And this potential can be maintained if you keep trowing objects towards the slide. (same as electrons continuously going in magnetic field)
 
Here is an excellent explanation of how a Hall effect sensor works:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html

It may be of interest that a commercially available Hall-effect sensor that can measure the earth’s magnetic field exist, and connect directly to your laptop, etc.

Magnetic Field Sensor
http://www2.vernier.com/booklets/mg.pdf
 
If the hall device is already there and switched on, the action of turning on the magnetic field will require a small but finite amount of energy extra than if the device were not switched on. This is a 'one off' input of energy, though and not an ongoing requirement for extra Power to be supplied by the magnet coils.