Module 2 : Normal metals
Lecture 2 : Magnetic susceptibility and Hall effect followed by problem solving
 
Hall effect
The Hall effect is used to determine the concentration and nature of charge carriers in a material. In the standard Hall effect geometry, a magnetic field is applied perpendicular to the direction in which an ohmic current is flowing. Due to the Lorentz force on the charge carriers, a voltage develops along the third orthogonal direction and is called the Hall voltage. The Hall coefficient is defined as $R_{H}=\frac{E_{y}}{j_{x}B_{z}}$ where $j_{x}$ is the ohmic current density in the $x$-direction, $B_{z}$ is the applied magnetic field in the $z$-direction, and$y$ is the electric field that is developed in the $y$-direction. The Hall coefficient is equal to $-\frac{1}{ne}$ (MKS units) if the charge carriers are electrons (of charge e and density n). A typical value of the Hall coefficient in metals is $10^{-10}\frac{\mathrm{m}^{3}}{\mathrm{C}}$. In contrast to the above, there are qualitative changes that take place in the properties of materials when they become superconducting. These will be elaborated at appropriate places when the properties of superconductors are discussed.