INTRODUCTION
HE HALL EFFECT occurs when a transverse
magnetic field is applied to a current-carrying conductor
resulting in an electric field which is perpendicular
to the directions of both the magnetic field and the
current and is proportional to their product (Fig. 1).
It was discovered in 1879 by Hall[’] who questioned Maxwell’s
earlier assertion that the “. . . mechanical force
which urges a conductor carrying a current across the
lines of magnetic force, acts, not on the electric current,
but on the conductor which carries This view,
however, was in contrast to the known fact that such a
force is proportional to the magnitude of the current and
is independent of the shape of the conductor. Hall, using a
gold leaf mounted on a plate of glass, was able to show
that an electromotive force existed in a direction per
pendicular to the directions of the current and of the
magnetic field. Since his work preceded the discovery of
the electron, he attributed the existence of this potential t,o
the rearrangement of the lines of current flow.
The physical significance of the Hall effect becomes
apparent when the current is considered to be a stream of
electrons moving through the solid. An electron traveling
in a magnetic field B with a velocity v experiences the
Lorentz force
F = e(v X B). (1)
Since the current is constrained by the boundaries of the
solid, electrons will at first be deflected by the magnetic
flux density B; soon enough, however, build-up of the
charges toward one side of the solid will create an elect,ric
field which will counterbalance the Lorent,z force acting on
the bulk of tshe current carriers and the current will
continue to flow in itms original direction as if unaffected by
the magnetic field. The time required to reach this equilibrium
is of the order of second. The electric field,
known as the Hall field, is therefore given by
EH = v X B. (2)
If the current density i = nev (n and e being the density
and charge of the carriers, respectively) is characterized by
a single electron velocity, the Hall field becomes
1
ne
E, = - &in (i, B).
INTRODUCTIONHE HALL EFFECT occurs when a transversemagnetic field is applied to a current-carrying conductorresulting in an electric field which is perpendicularto the directions of both the magnetic field and thecurrent and is proportional to their product (Fig. 1).It was discovered in 1879 by Hall[’] who questioned Maxwell’searlier assertion that the “. . . mechanical forcewhich urges a conductor carrying a current across thelines of magnetic force, acts, not on the electric current,but on the conductor which carries This view,however, was in contrast to the known fact that such aforce is proportional to the magnitude of the current andis independent of the shape of the conductor. Hall, using agold leaf mounted on a plate of glass, was able to showthat an electromotive force existed in a direction perpendicular to the directions of the current and of themagnetic field. Since his work preceded the discovery ofthe electron, he attributed the existence of this potential t,othe rearrangement of the lines of current flow.The physical significance of the Hall effect becomesapparent when the current is considered to be a stream ofelectrons moving through the solid. An electron travelingin a magnetic field B with a velocity v experiences theLorentz forceF = e(v X B). (1)Since the current is constrained by the boundaries of thesolid, electrons will at first be deflected by the magneticflux density B; soon enough, however, build-up of thecharges toward one side of the solid will create an elect,ricfield which will counterbalance the Lorent,z force acting onthe bulk of tshe current carriers and the current willcontinue to flow in itms original direction as if unaffected bythe magnetic field. The time required to reach this equilibriumis of the order of second. The electric field,known as the Hall field, is therefore given byEH = v X B. (2)If the current density i = nev (n and e being the densityand charge of the carriers, respectively) is characterized bya single electron velocity, the Hall field becomes1neE, = - &in (i, B).
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