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).