### Hall effect; Magnetism

Hall Effect: Lorentz force, electric and magnetic. Electric current density from density of electrons. Lorentz magnetic force on -e and on +e. Surface charges result.

Total Lorentz Force in y-direction zero. This condition gives an equation for the y-component of the electric field, which determines how much surface charge can be collected until the equillibrium is reached. Conventionally, the RH expression is constructed from measurable quantities. In the simple theory, this is simply related to the elementary electon charge density

Real life RH (table from Hemmers book). Hall effect used in Hall probes for measuring magnetic fields. Simple Drude model not sufficient, Hall effect with mobilities. Current jx treated as result of both hole and electron motion. Electrons and holes different mobilities. (compare with the drawings for surface charges) Convention for mobilities and velocities. Equillibrium when the currents caused by electric + magnetic forces cancel in y-direction. The jx must be a result of Ex. Ex will be eliminated.

Combining all the relations, using the last expression for the Ex in the velocities. Using the equation jy=0, inserting and rearranging. A relation similar to the Drude-type, but now with densities and mobilities. A new expression for RH is obtained. When n+=0, the electron-only relation s recovered.

On magnetism: vector potential for magnetic field strenth (induction). Relations for scalar and vector potential. curl of B related to current (if now time change of electric field.

Magnetic dipole moment: of current distribution. Compared to electric dipole moment. Vector potential of a magnetic dipole moment located at a distant x0

Interaction energy of a magnetic dipole moment with an external magnetic field B. It is minimum ("largest negative") if the moment and field are parallel. About the units: the SI units have an extra basic quantity: only three are necessary. In fact, the electromagnetics only contains combinations of e2, which has the dimension (Energy x length).