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Physical Principles of Sensing
• 3.1 Electric Charges, Fields, and Potentials
• 3.2 Capacitance
– 3.2.1 Capacitor
– 3.2.2 Dielectric Constant
• 3.3 Magnetism
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3.3.1 Faraday’s Law
3.3.2 Solenoid
3.3.3 Toroid
3.3.4 Permanent Magnets
• 3.4 Induction
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3.5 Resistance
3.5.1 Specific Resistivity
3.5.2 Temperature Sensitivity
3.5.3 Strain Sensitivity
3.5.4 Moisture Sensitivity
• 3.6 Piezoelectric Effect
– 3.6.1 Piezoelectric Films .
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3.7 Pyroelectric Effect
3.8 Hall Effect
3.9 Seebeck and Peltier Effects
3.10 SoundWaves
3.11 Temperature and Thermal Properties of Materials
– 3.11.1 Temperature Scales
– 3.11.2 Thermal Expansion
– 3.11.3 Heat Capacity
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3.12 Heat Transfer
3.12.1 Thermal Conduction
3.12.2 Thermal Convection
3.12.3 Thermal Radiation
3.12.3.1 Emissivity
3.12.3.2 Cavity Effect
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3.13 Light
3.14 Dynamic Models of Sensor Elements
3.14.1 Mechanical Elements
3.14.2 Thermal Elements
3.14.3 Electrical Elements
3.14.4 Analogies
This chapter examines various physical effects that can be
used for a direct conversion of stimuli into electric signals.
Electric Charges, Fields, and Potentials
triboelectric effect, which is a process of an electric
charge separation due to object movements, friction of
clothing fibers, air turbulence, atmosphere electricity, and
so forth.
He named one charge negative and the other positive.
Thunderstorm-electricity-friction
Atriboelectric effect is a result of a mechanical
charge redistribution. For instance, rubbing a glass rod
with silk strips electrons from the surface of the rod, thus
leaving an abundance of positive charges
• Be noted that the electric charge is conserved: It is
neither created nor destroyed.
• Electric charges can be only moved from one place
to another. Giving negative charge means taking
electrons from one object and placing them onto
another (charging it negatively).
• The object which loses some amount of electrons
is said gets a positive charge.
• A triboelectric effect influences an extremely small
number of electrons as compared with the total
electronic charge in an object.
• let us consider the total number of electrons in a
U.S. copper penny
• The coin weighs 3.1 g; therefore, it can be shown
that the total number of atoms in it is about
2.9×1022
• positive nuclear charge of 4.6×10−18 C and the
same electronic charge of the opposite polarity
• A combined charge of all electrons in a penny is
q =(4.6×10−18C/atom)(2.9×1022atoms)=1.3×105 C
• This electronic charge from a single copper penny
may generate a sufficient current of 0.91 A to
operate a 100-W light bulb for 40 h.
• electric charges
-conductors, isolators, and Semiconductors.
• In conductors, electric charges (electrons) are free
to move through the material, whereas in isolators,
they are not. many materials are considered
perfect isolators.
• The semiconductors are intermediate between
conductors and isolators in their ability to conduct
electricity.
• In semiconductors, the electrical conductivity may
be greatly increased by adding small amounts of
other elements; traces of arsenic or boron are
often added to silicon for this purpose.
(A)Positive test charge in the vicinity of a charged object and(B)the electric field of a spherical object.
• In this figure shows an object which carries a positive electric charge q.
• If a small positive electric test charge q0 is positioned in the vicinity of a charged
object, it will be subjected to a repelling electric force.
• If we place a negative charge on the object, it will attract the test charge.
• In vector form, the repelling (or attracting) force is shown as f .
• The boldface indicates a vector notation.
• A fact that the test charge is subjected to force without a physical contact
between charges means that the volume of space occupied by the test charge
may be characterized by a so-called electric field.
• The electric field in each point is defined through the force as E= f /q0
.
• Here ,E is vector in the same direction as f because q0 is
scalar. Formula (3.1) expresses an electric field as a force
divided by a property of a test charge.
• field lines which in every point of space are tangent to the
vector of force. By definition, the field lines start on the
positive plate and end on the negative. The density of
field lines indicates the magnitude of the electric field E in
any particular volume of space.
• field is a physical quantity that can be specified
simultaneously for all points within a given region of
interest
• Examples are pressure field, temperature fields, electric
fields, and magnetic fields. A field variable may be a scalar
• (e.g. Temperature field) or a vector (e.g., a gravitational
field around the Earth).
• A vector field may be characterized by a
distribution of vectors which form the so-called
flux (.).
• Flux is a convenient description of many fields,
such as electric, magnetic, thermal, and so
forth.
• A familiar analogy of flux is a stationary, uniform
field of fluid flow (water) characterized by a
constant flow vector v, the constant velocity of
the fluid at any given point. If we replace v by E
(vector representing the electric field), the field
lines form flux.
If we imagine a hypothetical closed surface (Gaussian
surface) S, a connection between the charge q and
flux can be established as ε0 =q,
where ε0 =8.8542×10−12 C2/N m2 is the permittivity
constant, or by integrating flux over the surface,
integral is equal to . In the above equations, known
as Gauss’ law charge q is the net charge surrounded
by the Gaussian surface the net flux is zero The
charge outside the surface makes no contribution to
the value of q
• Gauss’ law can be used to make an important
prediction, namely an exact charge on an insulated
conductor is in equilibrium, entirely on its outer
surface.
• Coulomb’s law itself can be derived from Gauss’
law. It states that the force acting on a test charge
is inversely proportional to a squared distance
from the charge:
• If the electric charge is distributed along an infinite
(or, for the practical purposes, long) line (Fig.A),
the electric field is directed perpendicularly to the
line and has the magnitude
Electric field around an infinite line (A) and near an infinite sheet (B). A pointed conductor
concentrates an electric field (C).
where r is the distance from the line and λ is the linear charge density (charge per unit
length). The electric field due to an infinite sheet of charge (Fig. 3.2B) is perpendicular
to the plane of the sheet and has magnitude
where σ is the surface charge density (charge per unit area). However, for an isolated
conductive object, the electric field is two times stronger:
A very important consequence of Gauss’ law is that electric charges are distributed only on the
outside surface.
This is why pointed conductors are the best concentrators of the electric field.
Faraday cage: a room entirely covered by either grounded conductive sheets or a
metal net. No matter how strong the external electric field, it will be essentially zero
inside the cage.
Electric dipole (A); an electric dipole in an electric field is subjected to a rotating force (B).
a perfect shield against electric fields, is of little use to protect against magnetic
fields, unless it is made of a thick ferromagnetic material.
An electric dipole is a combination of two opposite charges placed at a distance 2a
apart (Fig. 3.3A). Each charge will act on a test charge with force which defines
electric fields E1 and E2 produced by individual charges. A combined electric field of
a dipole, E, is a vector sum of two fields. The magnitude of the field is
If we measure E at various distances from the electric dipole
(assuming that the distance is much longer than a), we can
never deduce q and 2a separately, but only the product 2qa.
For instance, if q is doubled and a is cut in half, the electric
field will not change. The product 2qa is called the electric
dipole moment p. Thus, Eq. (3.10) can be rewritten as
The spatial position of a dipole may be specified by
its moment in vector form: p.
Gases such as methane On the other hand, carbon monoxide has a
weak dipole moment (0.37×10−30Cm) and water has a strong dipole
moment (6.17×10−30C m). When a dipole is placed in an electric field,
it becomes subjected to a rotation force Torque, which acts on a
dipole in a vector form, is
potential energy U in the system
consisting of the dipole and the arrangement used to set up the
external field. In a vector form this potential energy is
• A process of dipole orientation is called poling. the material during
the poling is heated to increase the mobility of its molecular
structure. The poling is used in fabrication of piezoelectric and
pyroelectric crystals.
• To find the voltage between two arbitrary points, we may use the
same technique as above—a small positive test charge q0. If the
electric charge is positioned in point A, it stays in equilibrium, being
under the influence of force q0E. Theoretically, it may remain there
infinitely long. Now, if we try to move it to another point B, we have
to work against the electric field. Work (WAB) which is done against
the field (that is why it has negative sign) to move the charge from
A to B defines the voltage between these two points:
The electrical potential at point B is smaller than at point A the electric potential
at that point is considered to be zero. This allows us to define the electric
potential at any other point as
If we travel through the electric field along a straight
line and measure V as we go, the rate of change of V
with distance l that we observe is the components of
E in that direction
The minus sign tells us that E points in the direction of
decreasing V . Therefore, the appropriate units for electric
field is volts/meter (V/m).
Capacitance
• take two isolated conductive objects of arbitrary shape
(plates) and connect them to the opposite poles of a
battery
• The plates will receive equal amounts of opposite charges; that is, a
negatively charged plate will receive additional electrons while
there will be a deficiency of electrons in the positively charged
plate.
• Now, let us disconnect the battery. If the plates are totally isolated
and exist in a vacuum, they will remain charged theoretically
infinitely long.
• A combination of plates which can hold an electric charge is called
a capacitor.
• If a small positive electric test charge, q0, is positioned between the
charged objects, it will be subjected to an electric force from the
positive plate to the negative.
• The positive plate will repel the test charge and the negative plate
will attract it, resulting in a combined push-pull force.
• Depending on the position of the test charge between the
oppositely charged objects, the force will have a specific magnitude
and direction, which is characterized by vector f .
Electric charge and voltage define the capacitance between two objects (A); a parallelplate capacitor (B).
The capacitor may be characterized by q, the magnitude of the charge on
either conductor (shown in Fig. A), and by V , the positive potential difference
between the conductors. It should be noted that q is not a net charge on the
capacitor, which is zero. Further, V is not the potential of either plate, but the
potential difference between them. The ratio of charge to voltage is constant
for each capacitor:
This fixed ratio, C, is called the capacitance of the capacitor. Its
value depends on the shapes and relative position of the plates.
C also depends on the medium in which the plates are
immersed. Note that C is always positive because we use the
same sign for both q and V . The SI unit for capacitance is 1
farad = 1 coulomb/volt, which is represented by the
abbreviation F. A farad is a very large capacitance; hence, in
practice submultiples of the farad are generally used:
1 picofarad (pF) =10−12 F
1 nanofarad (nF) =10−9 F
1 microfarad (μF) =10−6 F
• When connected into an electronic circuit, capacitance may be
represented as a “complex resistance”:
• where j = √−1 and i is the sinusoidal current having a frequency of ω,
• Meaning that the complex resistance of a capacitor drops at higher
frequencies. This is called Ohm’s law for the capacitor. The minus sign
and complex argument indicate that the voltage across the capacitor
lags 90◦ behind the current.
• It can be successfully applied to measure distance, area, volume,
pressure, force, and so forth.
• The electric field between the plates will be uniform, which means
that the field lines (lines of force f )
• Capacitor
• To calculate the capacitance, we must relate V , the potential
difference between the plates, to q, the capacitor charge :
• Alternatively, the capacitance of a flat capacitor can be found from
Cylindrical capacitor (A); capacitive displacement sensor (B).
• A cylindrical capacitor, shown in Fig. A, consists of two coaxial
cylinders of radii a and b and length l. For the case when lb, we
can ignore fringing effects and calculate capacitance from the
following formula:
• In this formula, l is the length of the overlapping conductors (Fig.
B) and 2πl[ln(b/a)]−1 is called a geometry factor for a coaxial
capacitor. A useful displacement sensor can be built with such a
capacitor if the inner conductor can be moved in and out of the
outer conductor. According to Eq. , the capacitance of such a
sensor is in a linear relationship with the displacement, l.