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I'm currently trying to understand the resistivity and conductivity tensor of a 2D sample. If a current carrying metal bar is placed inside a magnetic field the Hall Effect comes into play. I tried to search for explanations on how to obtain the resistivity tensor of the metal bar in this configuration but I can seem to understand how it is obtained.

Secondly, I have read that there should be a classical $$ B^2 $$ dependence of the resistance of the sample but I also do not understand what is the origin.

Thanks in advance!