## Hall Effect (Voltage, Hall Coefficient, Current, B-Field)

` $$ U_{\text H} ~=~ A_{\text H} \, \frac{I \, \class{violet}{B}}{d} $$ `

` $$ U_{\text H} ~=~ A_{\text H} \, \frac{I \, \class{violet}{B}}{d} $$ `

Explanation of what the Hall effect is, how exactly the Hall voltage is generated and how you can calculate it and the Hall constant.

` $$ U_\text{H} ~=~ \frac{1}{n \, q} ~ \frac{I \, \class{violet}{B}}{d} $$ `

Learn what the Hall effect is, how the Hall voltage is generated in a current-carrying bar in a magnetic field, and how this voltage is derived.

Here you will learn the basics of solid state physics - that is, electrical / thermal transport in solid matter, its crystal structure and interactions.

` $$ D(W) ~=~ \frac{L}{\pi} \, \left(\frac{2m}{\hbar^2}\right)^{1/2} \, \frac{1}{\sqrt{W}} $$ `

` $$ D(W) ~=~ \frac{V}{2\pi^2} \, \left(\frac{2m}{\hbar^2}\right)^{3/2} \, \sqrt{W} $$ `

` $$ D ~=~ \frac{A}{\pi} \, \frac{2m}{\hbar^2} $$ `

Here you will learn how to derive the 1d, 2d, and 3d density of states of a free electron gas from the k-volume and the dispersion relation.

` $$ E_{\text g} ~=~ 1.522\,\text{eV} - \frac{ 5.8 \cdot 10^{-4} \, \frac{ \text{eV} }{ \text{K} } \, T^2 }{ 300 \,\text{K} + T } $$ `

` $$ E_{\text g} ~=~ 0.742\,\text{eV} - 3.90 \cdot 10^{-4} \, \frac{ \text{eV} }{ \text{K} } \cdot T $$ `

` $$ E_{\text g} ~=~ 1.165\,\text{eV} - 2.84 \cdot 10^{-4} \, \frac{ \text{eV} }{ \text{K} } \cdot T $$ `