The Linear Hall Effect

A new method for handling the Boltzmann equation is used to obtain, without approximation, a general formula for the linear Hall effect in a solid electronic conductor. Expressions for the conductivity in no magnetic field and for the quadratic magnetoconductivity are also obtained. These formulas introduce a vector mean free path, not in general parallel to the electron velocity, which is related to the velocity by an integral equation. Some possible cases of the formula for the Hall effect are analyzed. The solution of the integral equation for the vector mean free path is discussed, and methods of approximation are proposed.