Transcript The Hall Effect

The Hall Effect
AP Physics
Montwood High School
R.Casao
• When a current-carrying conductor is placed in
a magnetic field, a voltage is generated in a
direction perpendicular to both the current and
the magnetic field.
• The Hall Effect results from the deflection of
the charge carriers to one side of the conductor
as a result of the magnetic force experienced
by the charge carriers.
• The arrangement for observing the Hall Effect
consists of a flat conducting strip carrying a
current I in the x-direction.
• A uniform magnetic field B
is applied in the y-direction.
• If the charge carriers are
electrons moving in the
negative x-direction with a
velocity vd, they will
experience an upward
magnetic force FB.
• The electrons will be
deflected upward, making
the upper edge negatively
charged and the lower edge
positively charged.
• The accumulation of charge at the edges
continues until the electric field and the
resulting electric force set up by the charge
separation balances the magnetic force on the
charge carriers (Fmag = Felectric).
• When equilibrium is reached, the electrons are
no longer deflected upward.
• A voltmeter connected across the conductor can
be used to measure the potential difference
across the conductor, known as the Hall voltage
VH.
• When the charge carriers are positive, the
charges experience an upward magnetic force
q·(v x B).
• The upper edge of the conductor becomes
positively charged, leaving the bottom of the
conductor negatively charged.
• The sign of the Hall voltage generated is
opposite the sign of the Hall voltage resulting
from the deflection of electrons.
• The sign of the charge carriers can be
determined from the polarity of the Hall
voltage.
• When equilibrium is reached between the
electric force q·E and the magnetic force
q·vd·B, the electric field produced between the
positive and negative charges is referred to as
the Hall field, EH, therefore, q·EH = q·vd·B.
• EH = vd·B
• If d is taken to be the width of the
conductor, then the Hall voltage VH
measured by the voltmeter is:
VH  EH  d  vd  B  d
• The measured Hall voltage gives a
value for the drift velocity of the
charge carriers if d and B are known.
• The number of charge carriers per unit
volume (charge density), n, can also be
determined by measuring the current in
the conductor:
I
IBd
vd 
VH 
nq  A
nq  A
• Area A = thickness t·d, therefore:
IB
VH 
nq t
• Hall coefficient, RH =
1
n q
• The Hall coefficient can be determined from
IB
RH  I B
VH 

n qt
t
• The sign and magnitude of RH gives the sign of the
charge carriers and their density.
• In most metals, the charge carriers are electrons and
the charge density determined from the Hall effect
measurements agrees with calculated values for
metals which release a single valence electron and
charge density is approximately equal to the number
of valence electrons per unit volume.
Legend:
1. Electrons
(not conventional current)
2. Hall element, or Hall sensor
3. Magnets
4. Magnetic field
5. Power source
In drawing "A", the Hall element
takes on a negative charge at the top
edge (symbolized by the blue color)
and positive at the lower edge (red
color).
In "B" and "C", either the electric
current or the magnetic field is
reversed, causing the polarization to
reverse. Reversing both current and
magnetic field (drawing "D") causes
the Hall element to again assume a
negative charge at the upper edge.