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Illustration Hall Plate with illustrated Dimensions, Hall Voltage and Forces

Hall plate with holes Hall effect with Electrons Hall effect with Electrons and Holes Square Hall Plate with Dimensions Current-carrying Hall plate with Electrons Forces on an electron due to Hall effect
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A current \( I \) is applied to a sample (consisting of a metal or semiconductor) of length \(L\), height \(h\), and thickness \(d\) along the sample so that the free electrons move along the sample from one end to the other end at the drift velocity \(v\).

The sample is in an external magnetic field B applied perpendicularly to the sample. As a result, the electrons experience a magnetic force \( F_{\text m} \) (Lorentz force), which in this case deflects the electrons to the upper part of the sample. This results in a negative excess charge in the upper part of the sample and a positively charged region in the lower part. The deflection continues until the opposing electric force \( F_{\text e} \) balances the magnetic force (equilibrium).

Thus, a voltage is generated across the sample, which is called Hall voltage. Its sign differs depending on whether the charge transport is dominated by negative or positive charge carriers.