# Illustration Hall Plate with illustrated Dimensions, Hall Voltage and Forces

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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.