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Transcript LECTURE 13

As already explained in- Art 14.12 page 562, when a conductor
is kept perpendicular to the magnetic field and a direct current
is passed through it, it results in an electric field perpendicular
to the directions of both the magnetic field and current with a
magnitude proportional to, the product of the magnetic field
strength and current. The voltage so developed is very small
and it is difficult to detect it. But in some semiconductors such
as germanium, this voltage is enough for measurement with a
sensitive moving coil instrument. This phenomenon is called
the Hall effect and is explained below.
Let us consider a slab of conducting material connected to a
battery so that a current I flows through the slab in the manner
shown in fig. The electrons constituting the flow of current I
actually flow in the direction opposite to that of conventional
current. Now no potential difference exists between the top and
bottom of the slab, as shown in fig. (12), because no transverse
magnetic field passes through the slab.
• Fig (12) Hall Effect
• When the magnetic field is applied so that it is
perpendicular to the slab of Hall crystal, the electrons are
acted on by a force because of magnetic field. The force
acts in a vertical direction, and the electrons are forced
toward the top of the slab. This results in an excess of
electrons near the top of the slab and a deficiency of
electrons near the bottom. Thus a potential difference is
created between the top and bottom of the slab. The
magnitude of this voltage is proportional to the product of
strength of the magnetic field and current flowing through
the slab and is given by the expression
VH 
• where I is the current flowing through the slab in amperes, B is the
flux density of the magnetic field applied in wb/m2, t is the thickness
of slab in metre, and kH is the Hall effect coefficient and is inversely
proportional to the carrier density in the solid. So the Hall effect is
much more pronounced in semiconductors than in metals. Thus the
voltage reading across the device can be calibrated to give the
magnetic field strength directly in case the current glowing through
the conducting slab is known. Hall-effective transducers can be built
to be sensitive enough to detect very small magnetic fields.
• Commercial Hall-effect transducers are made from
germanium or other semiconductor materials. They find
application in instruments that measure magnetic field
with small flux densities.
• Hall effect element can be used for measurement of
current by the magnetic field produced due to flow of
• Hall effect element may be used for measuring a linear
displacement or location of a structural element in cases
where it is possible to change the magnetic field strength
by variation in the geometry of a magnetic structure. For
example, an arrangement illustrated in fig. (13).
Fig (13) Hall Effect Displacement Transducer •
• The Hall effect element is located in the gap, adjacent to
the permanent magnet and the field strength produced in
the gap, due to the permanent magnet, is changed by
changing the position of the ferromagnetic plate. The
voltage output of the Hall effect element is proportional
to the field strength of the gap which is a function of the
position of ferromagnetic plate with respect to the
• Thus displacement can be measured by the Hall effect
transducer. Very small displacements (as small as 0.025
mm) can be measured by this method.
• The arrangement for measuring small rotary shaft displacements
with the use of Hall effect element is illustrated in fig. (14).
• The Hall effect element is rigidly suspended between the poles of a
permanent magnet fixed to the shaft, as illustrated in fig. The
element remains stationary when the shaft rotates. With a constant
current I supplied to the element, the voltage output (Hall voltage
VH) across the element is directly proportional to the sine of angular
displacement of the shaft and for smaller angular displacements
(say t 5° of rotation) the output voltage will be directly proportional to
the angular displacement, thereby giving linear scale.
• The main advantage of Hall effect transducers is that they are noncontact devices with small site and high resolution.
• The main drawbacks of these transducers are high sensitivity to
temperature changes and variation of Hall coefficient from plate to
plate, thereby requiring individual calibration in each case.
• Fig (14 ) Hall Effect Angular Displacement Transducer
• Example. An Hall effect element used for
measuring a magnetic field strength gives
on output voltage of 10.5 mV. The element
is made of silicon and is 2.5 mm thick and
carries a current of 4 A. The Hall
coefficient for is 4.1 x 10-6 Vm/A-wb/m2.
• Solution: Hall effect element thickness, t = 2.5mm = 2.5 x 10-3m
Output voltage, VH = 10.5 mV= 10.5 x 10-3 V
Current, I = 4 A
• Hall coefficient, kH = 4.1 x 10-6 Vm/A-wb/m2
Magnetic field strength, B
10.5 x 10  3 x 2.5 x 10 3
4.1 x10 x4