electricity & magnetism (fall 2011) lecture # 2 by moeen ghiyas
TRANSCRIPT
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ELECTRICITY & MAGNETISM (Fall 2011)
LECTURE # 2
BY
MOEEN GHIYAS
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TODAY’S LESSON
(Chapter 1 – Physical Measurements, Atomic Structure
Chapter 22 / 23 – Electric Charge)
Fundamentals of Physics by Halliday / Resnick / Walker
(6th / 7th Edition)
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Today’s Lesson Contents
• Lengths, Mass and Time – Some Measured Values
• Some Physical Properties
• The Greek Alphabets
• The Building Block of Matter
• Valence & Free Electron
• Ions
• Electric Charge and its Properties
• Quantization of Electric Charge
• Coulomb’s Law
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Lengths – Some Measured Approximate Values
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Some Physical Properties
• Distance to
– Moon = 3.82 x 108 m
– Sun = 1.50 x 1011 m
– Nearest star = 4.04 x 1016 m
– Galactic centre = 2.2 x 1020 m
– Edge of the observable universe = ~ 1026 m
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Masses – Various Bodies (Approximate Values)
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Time – Approximate Values of Some Time Intervals
Age of Universe = in years?
= 5 x 1017 / (60x60x24x365) = 158 billion years
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Some Physical Properties
• Air (dry, at 200C and 1 atm)
– Speed of sound = 343 m/s
– Electrical Breakdown strength = 3 x 106 V/m
• Water
– Speed of sound = 1460 m/s
• Earth
– Mass = 5.98 x 1024 kg
– Mean radius = 6.37 x 106 m
– Period of satellite at 100 km altitude = 86.3 min
– Radius of geosynchronous orbit = 42,200 km
– Escape speed = 11.2 km/s
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The Greek AlphabetsName Capital Small Name Capital Small
Alpha Α α Nu Ν ν
Beta Β β Xi Ξ ξ
Gamma Γ γ Omicron Ο ο
Delta Δ δ Pi Π π
Epsilon Ε ε Rho Ρ ρ
Zeta Ζ ζ Sigma Σ σ
Eta Η η Tau Τ τ
Theta Θ θ Upsilon Υ υ
Iota Ι ι Phi Φ φ
Kappa Κ κ Chi Χ χ
Lambda Λ λ Psi Ψ ψ
Mu Μ μ Omega Ω ω
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The Building Block of Matter
• Let us review briefly the structure of matter.
• What if the pieces of any matter say gold are
cut indefinitely? The two Greek philosophers
Leucippus and his student Democritus —
could not accept the idea that such cuttings
could go on forever.
• They speculated that the process ultimately
must end when it produces a particle that can
no longer be cut.
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The Building Block of Matter
• In Greek, atomos means “not
sliceable.” From this comes our
English word atom.
• To really understand electricity, we
must “break the atom down” into
smaller particles.
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The Building Block of Matter
• All ordinary matter consists of atoms, and each
atom is made up of electrons surrounding a
central nucleus.
• Following the discovery of the nucleus in 1911,
the question arose: Does it have a structure?
• The exact composition of the nucleus is not
known completely even today, but by the early
1930s a model evolved that helped us
understand how the nucleus behaves.
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Atomic Structure
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3 Major Parts Of An Atom
• Proton
• Neutron
• Electron
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Electric Charge Location in an Atom
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Electron
• Electrons are negatively charged particles that
surround the atom's nucleus. Electrons were
discovered by J. J. Thomson in 1897.
• Electrons determine properties of the atom.
Chemical reactions involve sharing or
exchanging electrons.
• Electrons are responsible for electric current
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Proton
• Protons are positively charged particles found
in the atomic nucleus. Protons were
discovered by Ernest Rutherford..
• Experiments done in the late 1960's and early
1970's showed that protons are made from
other particles called quarks.
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Neutron
• Neutrons are uncharged particles found in the
atomic nucleus. Neutrons were discovered by
James Chadwick in 1932.
• Experiments done in the late 1960's and early
1970's showed that neutrons are also made
from other particles called quarks
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The Building Block of Matter
• What is the role of neutron in an atom and
matter as a whole?
• Neutrons act as glue (adding mass to nucleus
for gravitational force to strengthen).
• If neutrons were not present in the nucleus,
the repulsive force between the positively
charged particles would cause the nucleus to
come apart.
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The Building Block of Matter
• Protons, neutrons, and a host of other exotic
particles are now known to be composed of
particles called quarks.
• Protons comprise of 2 up & 1 down quarks
• Neutrons comprise of 1 up & 2 down quarks
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The Building Block of Matter – (Quark)• Quarks were first discovered in experiments done in the
late 1960's and early 1970's.
• Three families of quarks each having two types are known
to exist i.e. a total of six types of quarks have been
discovered.
• The first family consists of Up and Down quarks, the
quarks that join together to form protons and neutrons.
• The second family consists of Strange and Charm quarks
and only exist at high energies.
• The third family consists of Top and Bottom quarks and
only exist at very high energies.
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The Building Block of Matter
• Why protons have +ve charge and neutrons are
neutral?
• The up, charm, and top quarks have charges +⅔
of that of the proton, whereas the down,
strange, and bottom quarks have charges -⅓ of
that of the proton. Thus,
• Proton = + ⅔ + ⅔ - ⅓ = + 4∕3 - ⅓ = +3∕3 = +1 charge
• Neutron = +⅔ - ⅓ - ⅓ = + ⅔ - ⅔ = 0 charge
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The Building Block of Matter• Electron – What is its orbit shape?
• Electrons revolve around nucleus in elliptical path and
each electron has its own orbit (elliptical path).
• Comparative size and weight ?
• The electron is nearly 2000 times larger but at the same
time nearly 1∕2000 times lighter than either the proton or
neutron. Thus nucleus of an atom contains most of the
weight, while electrons make up the volume.
• Distance between nucleus and electron?
• Distance between nucleus and electron is approximately
60,000 times greater than diameter of the electron.
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The Building Block of Matter• ANALOGY of a simplest atom i.e. the hydrogen atom, which
contains one electron , one proton and no neutrons
• Let nucleus be represented by a common marble
• The electron then could be represented by 100 feet / 31 meter ball
• Electron revolves that marble at a distance of 1000 miles / 1610
km.
• However, remember that sizes and distances are sub-microscopic
e.g. diameter of an electron is only 4x10–13 cm.
++–– ++––
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Valence Electron
• The electrons in the outermost shell / orbit are
called valence electrons.
• They get involved in chemical reactions and
are responsible for electric currents.
• Valence electrons are held to the nucleus with
less attraction than the electrons in inner
shells. Thus, valence electrons can be
removed from parent atom with more ease.
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Free Electrons• Free electrons are the valence electrons that have
been temporarily separated from an atom.
• They are free to wander about in the space around
the atom.
• A valence electron is freed from its atom when energy
is added to the atom.
• Energy can be provided by heating the atom or
subjecting it to electric field.
• A free electron carries more energy than it did as
valence electron.
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Ions
• When a valence electron leaves an atom to become a
free electron, it makes parent atom a +ve ion, due to
excess number of protons to electrons.
• Conversely, if an atom gains an electron it becomes a
–ve ion due to addition of an electric –ve charge of
added electron.
• The concept of ions is important in understanding
electric circuits involving batteries and gas filled
devices.
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Electric Charge & Its Properties
• Both electrons and protons possess electric charges of opposite
polarities i.e. –ve and +ve.
• These electric charges create electric fields of force that behave
much like magnetic fields of force.
–– ++
++––
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Electric Charge & Its Properties
• Like charges repel and unlike charges attract each other.
• When a glass rod is rubbed with silk, the silk obtains a negative
charge that is equal in magnitude to the positive charge on the
glass rod, while converse happens with fur rubbing a rubber rod.
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Electric Charge & Its Properties
• Electric charge is always conserved i.e.
when one object is rubbed against
another, charge is not created in the
process.
• The electrified state is due to a transfer
of charge from one object to the other.
One object gains some amount of
negative charge while the other gains an
equal amount of positive charge.
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Quantization of Electric Charge
• All experiments so far have shown that electric charge
in nature always occurs as some integral multiple of a
fundamental amount of charge ‘e’ (from electrons).
• The electron has a charge – e charge
• The proton has an equal magnitude +e charge.
• The neutron has 0 or no charge.
• This occurrence of charges in discrete units is called
charge quantization.
• The value of e = 1.602 x 10–19 coulombs (in SI Units)
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Quantization of Electric Charge
• In modern terms, the electric charge q is said to be quantized,
where q is the standard symbol used for charge i.e. electric
charge exists as discrete “packets,” and we can write
q = Ne, where N is some integer.
• Is it possible for us to find in nature following charges?
a. +10e
b. -6e
c. 3.57e
• However, recent theories propose the existence of particles
called quarks having charges – e/3 and +2e/3, but free quarks
have never been detected so far
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Coulomb’s Law
• Charles Augustine Coulomb (1736–1806)
measured the magnitudes of the electric
forces between charged objects using the
torsion balance, which he invented.
• The operating principle of the torsion
balance is the same as that of the
apparatus used by Cavendish to measure
the gravitational constant, with the
electrically neutral spheres replaced by
charged ones.
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Coulomb’s Law
• Coulomb’s experiments showed that the electric force between
two stationary charged particles
– is inversely proportional to the square of the separation r between
the particles and directed along the line joining them;
– is proportional to the product of the charges q1 and q2 on the two
particles;
– is attractive if the charges are of opposite sign and repulsive if the
charges have the same sign.
• Thus, magnitude of electrostatic force of attraction or repulsion
between two point charges can be defined by Coulomb’s Law as
• where ke is a constant called the Coulomb constant
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Coulomb’s Law
• Curiously, the Coulomb’s equation Fe = k x (q1 q2) / r2
is the same as Newton’s equation Fg = G x (m1 m2) / r2
for gravitational force between two particles with masses m1 and m2
separated by distance r, and where G is gravitational constant.
• Note: The laws differ in that gravitational forces are always attractive
but electrostatic forces may either be attractive or repulsive.
• Where the gravitational constant G = 6.7 x 10–11 Nm2/kg2
• And constant ke in SI units has the value ke = 8.9875 x 109 Nm2/C2
• This constant is also written in the form
• where the constant ε0 (lowercase Greek epsilon) is known as the
permittivity of free space and has the value 8.8542 x 10–12 C2/Nm2
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Charge and Mass of the Atomic Particles
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Electric Force vs Gravitational Force
• Example – The electron and proton of a hydrogen atom are
separated by a distance of approximately 5.3 x10–11 m. Find the
magnitudes of the electric force and the gravitational force between
the two particles.
• Solution
• From Coulomb’s law, we find that the attractive electric force has
the magnitude
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Electric Force vs Gravitational Force
• From Coulomb’s law, we find that the attractive electric force has the
magnitude
• Using Newton’s law of gravitation for the particle masses, we find that
the gravitational force has the magnitude
• The ratio Fe /Fg ≈ 2 x 1039. Thus, the gravitational force between
charged atomic particles is negligible compared to the electric force.
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Coulomb’s Law
• We know that force is a vector quantity.
• Thus, the coulomb’s law expressed in vector form for
the electric force exerted by a charge q1 on a second
charge q2 , written F12 , is
• where ȓ is a unit vector directed from q1 to q2 , as
shown in Fig a.
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Coulomb’s Law
• Note that electric force obeys Newton’s third law, thus
the electric force exerted by q2 on q1 is equal in
magnitude to the force exerted by q1 on q2 and in the
opposite direction; that is, F21 = – F12
• Noting the sign of the product q1q2 is an easy way of
determining the direction of forces acting on the
charges.
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Coulomb’s Law
• When more than two charges are present, the force
between any pair of them is given by coulomb’s
equation.
• While, the resultant force on any one of them equals
the vector sum of the forces exerted by the various
individual charges.
• For example, if four charges are present, then the
resultant force exerted by particles 2, 3, and 4 on
particle 1 is: F1 = F21 + F31 + F41
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Coulomb’s Law – Shell Theorems
• Theorem 1 – A shell of uniform charge attracts
or repels a charged particle that is outside the
shell as if all the shell’s charge were
concentrated at its centre.
• Theorem 2 – If a charged particle is located
inside a shell of uniform charge, there is no
net electrostatic force on the particle from the
shell.
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Coulomb’s Law
• Example – Consider three point charges located at
the corners of a right triangle as shown in figure,
where q1 = q3 = 5.0 μC, q2 = – 2.0 μC and a = 0.10m.
Find the resultant force exerted on q3 .
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Coulomb’s Law
• Solution F23 = ?
• F13 = ?
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Coulomb’s Law
• ....Solution
• Now F23 = 9 N and F13 = 11 N
• Is really F3 = F23 + F13 = ?
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Electric Forces in Use
• Many cosmetics also take advantage of electric forces by
incorporating materials that are electrically attracted to skin or
hair, causing the pigments or other chemicals to stay put once
they are applied.
• The plastic in many contact lenses, etafilcon, is made up of
molecules that electrically attract the protein molecules in
human tears.
• These protein molecules are absorbed and held by the plastic so
that the lens ends up being primarily composed of the wearer’s
tears. Because of this, the wearer’s eye does not treat the lens
as a foreign object, and it can be worn comfortably.
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Summary / Conclusion
• Lengths, Mass and Time – Some Measured Values
• Some Physical Properties
• The Greek Alphabets
• The Building Block of Matter
• Valence & Free Electron
• Ions
• Electric Charge and its Properties
• Quantization of Electric Charge
• Coulomb’s Law
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