Electrostatics and Magnetostatics
Fondamental : Action of a magnetic field on the movement of charge carriers
An electrical conductor under a voltage difference sees its carrier electrons set in motion.
The lesson about Ohm's local law specified the notations.
The electrical conductor is additionally placed in a magnetic field .
Newton's second law applied to a charge carrier is expressed by :
The following picture outlines the geometry of the conductor used : it is a parallelepiped rectangle of length .
The exterior magnetic field is .
The electric field created by the generator which sets charge carriers in motion is called .
In steady-state, electrons move with the velocity .
In steady-state ( ) :
The magnetic term is oriented as Ox axis. Thus an electric field appears, called the Hall field such as :
Thus, the speed of the carriers becomes :
This Hall field is induced by the motion of electrons during a brief moment (length of transitory regime) towards side (2).
This creates a dissymmetry of charges, thus an electric field oriented from side (1) to side (2).
Fondamental : Calculation of the Hall Voltage
The Hall electric field is :
The Hall voltage is obtained by calculating the line integral around a loop of the field :
The intensity of the current is :
If (carrier electrons case, with on the picture) :
Hence we can see the Hall voltage is proportional to the magnetic field that is applied.
Hall probes can measure this voltage and deduce the value of the magnetic field.
Complément : Laplace force
See the lesson about Laplace force.
Simulation : Animation JAVA de JJ.Rousseau (Université du Mans)
Hall probe : click HERE