(a) Show for a 2D Hall bar of length (L) and width (w) that (j=sigma E) (where...
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(a) Show for a 2D Hall bar of length \(L\) and width \(w\) that \(j=\sigma E\) (where \(j\) is the current density, \(E\) is the electric field, and \(\sigma\) is the conductivity) is equivalent to the simple form of Ohm's law, \(V=I R\). The resistance is \(R=ho L / w\), where \(ho=1 / \sigma\) is the resistivity.
(b) Show that for Fig. 28.1 the resistance components \(R_{i j}=V_{i} / I_{j}\) and resistivity components \(ho_{i j}=E_{i} / j_{j}\) are related by \(R_{y x}=ho_{y x}\) and \(R_{x x}=(L / w) ho_{x x}\).
(c) Verify the final forms of the \(ho\) and \(\sigma\) tensors in Box 28.1 .
Data from Fig. 28.1
Data from Box 28.1
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Related Book For
Symmetry Broken Symmetry And Topology In Modern Physics A First Course
ISBN: 9781316518618
1st Edition
Authors: Mike Guidry, Yang Sun
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