Hall effect

Introduction
Introduction
Introduction :
Hall Effect was discovered by "Edwin Herbert Hall" in 1879.
Hall Effect is a phenomenon in which a transverse electric field is
developed in a solid material when the material carrying an electric
current is placed in a magnetic field that is perpendicular to the
current.
The principle of Hall Effect states that when a current-carrying
conductor or a semiconductor is introduced to a perpendicular
magnetic field, a voltage can be measured at the right angle to the
current path.
This effect of obtaining a measurable voltage is known as the Hall
Effect.
Edwin Herbert Hall

Introduction
Introduction
Introduction :
Hall coefficient is defined as the ratio of the induced electric field to the product of the
current density and the applied magnetic field.
The potential difference produced across an electrical conductor when an external
magnetic field is applied perpendicular to the current through the conductor "Hall
Voltage".

Theory behind the Hall effect :
Electric Current is basically a flow of charged particles through a conductive path. These
charged particles may be ‘Negative Charged Electrons’ or even ‘Positive Charged Holes’
(voids where electrons should be).
If we take a thin conductive plate (as shown above in Fig 1 and reiterated below for ease
of reader) and connect it in a circuit with a battery (voltage source) then a current will start
flowing it. The charge carriers will flow in a straight line from one end of the plate to the
other end.
Fig. 1
Current Flowing Through a Plate

As the charge carriers are in motion, they will produce a magnetic field. Now when you
place a magnet near the plate, its magnetic field will distort the magnetic field of the charge
carriers. This will upset the straight flow of the charge carriers. The force which upsets the
direction of flow of charge carriers is known as Lorentz force.
Due to the distortion in the magnetic field of the charge carriers, the negative charged
electrons will be deflected to one side of the plate and positive charged holes to the other
side. That is why a potential difference (also called as Hall Voltage) will generate between
both sides of the plate which can be measured using a meter.
This effect is known as Hall Effect.
Fig. 2
Deflection of Electrons and Holes

Hall Voltage is directly proportional to Electric Current.
Hall Voltage is directly proportional to the applied magnetic field.
The stronger the magnetic field, the more the electrons will be deflected. This means that the
higher the current, the more the electrons will be deflected. And, the more the electrons will
be deflected, the more the potential difference will be observed between both sides of the
plate. Therefore we can say that:

Introduction
Introduction
Theory :
We know that the conduction in solids is due to the motion of the charge carriers under the
influence of an applied field. So, first we define the following terms:
Charge
Current density(J)
Conductivity
Resistivity
Carrier density
Electric field
Mobility
Effective mass
Drift velocity

Introduction
Introduction
Theory :
Charge :-
Electric charge is a scalar quantity.
Coloumb is the unit of electric charge.
Electric charge is the basic physical property of matter that causes it to experience a
force when kept in an electric or magnetic field.
The two types of electric charges are: Positive and Negative, commonly carried by charge
carriers protons and electrons.
“One coulomb is the quantity of charge transferred in one second.”
Mathematically, the definition of a coloumb is represented as:
Q = I.t

Introduction
Introduction
Theory :
Current density :-
The amount of electric current traveling per unit cross-section area is called as current
density and expressed in amperes per square meter.
The formula for Current Density is given as,
J = I / A
Where,
I = current flowing through the conductor in Amperes
A = cross-sectional area in m².
Current density is a vector quantity
Current density is expressed in A/m².

Introduction
Introduction
Theory :
Conductivity:-
Electrical conductivity is the measure of the capability of the material to pass the flow of
electric current. Electrical conductivity is denoted by the Greek letter ρ.
The Electrical conductivity is the inverse of the resistivity and is given by:
σ = 1/ρ
Where,
σ = electrical conductivity
ρ = resistivity
Electrical conductivity, a measure of a material's ability to conduct an electric current..
Ionic conductivity, electrical conductivity due to ions moving position in a crystal lattice.
Thermal conductivity, an intensive property of a material that indicates its ability to conduct heat.

Introduction
Introduction
Theory :
Resistivity:-
Electrical resistivity is the reciprocal of electrical conductivity. It is the measure of the ability of a
material to oppose the flow of current.
Metals are good conductors of electricity. Hence, they have low resistivity.
The insulators like rubber, glass, graphite, plastics, etc. have very high resistivity when
compared to the metallic conductors.
The third type is the semiconductor which comes in between the conductors and
insulators. Their resistivity decreases with the increase in temperature and is also affected
by the presence of impurities in them.
Materials having electric field and current density will have the following resistivity formula:
ρ=E/J

Introduction
Introduction
Theory :
Resistivity:-
Materials having electric field and current density will have the following resistivity formula:
ρ=E/J
Where,
ρ is the resistivity of the material in Ω.m
E is the magnitude of the electric field in V.m
J is the magnitude of current density in A.m
-1
-2
Where,
ρ is the resistivity of the material in Ω.m
R is the electrical resistance of uniform cross-sectional material in Ω
l is the length of a piece of material in m
A is the cross-sectional area of the material in m
Conductors with a uniform cross-section and uniform flow of electric current will have the
following resistivity formula:
2
ρ= R
l
A

Introduction
Introduction
Theory :
Carier density:-
The charge density is the measure of electric charge per unit area of a surface, or per unit
volume of a body or field.
The charge density tells us how much charge is stored in a particular field. Charge density can
be determined in terms of volume, area, or length.
Linear charge density;
where,
q is the charge
l is the length over which it is distributed
S.I unit of Linear charge density is coulomb/m
λ = q / l

Introduction
Introduction
Theory :
Carier density:-
Surface Charge Density;
where,
q is the charge
A is the area over which it is distributed
σ = q / A
2

Introduction
Introduction
Theory :
Carier density:-
Volume Charge Density;
where,
q is the charge
V is the volume over which it is distributed
ρ = q / v
3

Introduction
Introduction
Theory :
Electric field :-
Electric field can be considered as an electric property associated with each point in the
space where a charge is present in any form. An electric field is also described as the
electric force per unit charge.
The formula of electric field is given as;
E = F /Q
Where,
E is the electric field.
F is a force.
Q is the charge.

Introduction
Introduction
Theory :
Electric field :-
Electric fields are usually caused by varying magnetic fields or electric charges. Electric field
strength is measured in the SI unit volt per meter (V/m).
The direction of the field is taken as the direction of the force which is exerted on the positive
charge. The electric field is radially outwards from positive charge and radially in towards
negative point charge.

Introduction
Introduction
Theory :
Mobility:-
The drift velocity of an electron for a unit electric field is known as mobility of the electron.
Mobility of an electron can be calculated by:
where,
Vd is the drift velocity of an electron
E is the external electric field
μ = Vd/E

Introduction
Introduction
Theory :
Drift Velocity:-
The average velocity attained by charged particles, (eg. electrons) in a material due to an
electric field.
The SI unit of drift velocity is m/s. It is also measured in m /(V.s).
2
I = nAvQ
Where,
I, is the current flowing through the conductor which is
measured in amperes
n, is the number of electrons
A, is the area of the cross-section of the conductor which is
measured in m^2
v, is the drift velocity of the electrons
Q, is the charge of an electron which is measured in
Coulombs

Introduction
Introduction
Apparatus description :-
Experimental Setup
Two solenoids
Hall probe
Four probe
Digital gauss meter
Digital milli-voltmeter
Constant current supply

Introduction
Introduction
Theory :
Solenoids:-
A solenoid is a basic term for a coil of wire that we use as an electromagnet. We also refer
to the device that can convert electrical energy into mechanical energy as a solenoid.
Actually it generates a magnetic field for creating linear motion from the electric current.
With the use of a magnetic field.

Introduction
Introduction
Theory :
Hall Probe :-
A Hall probe is a device that uses a calibrated Hall effect sensor to directly measure the
strength of a magnetic field.
Since magnetic fields have a direction as well as a magnitude, the results from a Hall
probe are dependent on the orientation, as well as the position, of the probe.

Introduction
Introduction
Theory :
Digital Gauss meter :-
A Gauss Meter can measure the direction and the intensity of small (relatively) magnetic
fields.
For larger magnetic fields, a Tesla Meter, is used, which is similar, but it measures in larger
Tesla units.
A Gauss Meter comprises a gauss probe/sensor, the meter and a cable connecting both. The
Gauss Meter works on the basis of the Hall effect.

Introduction
Introduction
Theory :
Constant Current power Supply :-
Constant current : A constant current is a type of direct current (DC) that does not
change its intensity with time.
If the load is constant, a steady current can be obtained via a constant voltage source.
If the load is varying, a steady current can be obtained via a constant current supply
source.
A constant current system is one that varies the voltage across a load to maintain a
constant electric current.
When a component is indicated to be driven by a constant current, the driver circuit
is, in essence, a current regulator and must appear to the component as a current
source of suitable reliability.

Introduction
Introduction
Theory :
Constant Current power Supply :-
This electric field depends upon cross product of magnetic flux density [B] and current density [ J ].
R is called Hall Coefficient
Here, Ey is induced electric field
V is Hall voltage
B is magnetic flux density
jx is current density
n is charge carrier density
t is thickness of crystal
The hall coefficient is positive if the number of positive charge carriers is more than the negative
charge carriers. Similarly, it is negative when electrons are more than holes.
H
H

Introduction
Introduction
Results :
Hall Coefficient can be determined using
Hall effect can be used to determine the signs of
current carrier in metals and semiconductor.
A straight graph between Hall voltage & Current
and between Hall voltage & Magnetic field
confirms their linear relationship. This point has
important meaning as hall effect can be
effectively used to determine current or
magnetic field, when other is known.
Rh=Vhb/IH

Hall effect

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