electricity & magnetism (fall 2011) lecture # 2 by moeen ghiyas

ELECTRICITY & MAGNETISM (Fall 2011)

LECTURE # 2

BY

MOEEN GHIYAS

TODAY’S LESSON

(Chapter 1 – Physical Measurements, Atomic Structure

Chapter 22 / 23 – Electric Charge)

Fundamentals of Physics by Halliday / Resnick / Walker

(6th / 7th Edition)

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

Lengths – Some Measured Approximate Values

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

Masses – Various Bodies (Approximate Values)

Time – Approximate Values of Some Time Intervals

Age of Universe = in years?

= 5 x 1017 / (60x60x24x365) = 158 billion years

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

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

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.

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.

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.

Atomic Structure

3 Major Parts Of An Atom

• Proton

• Neutron

• Electron

Electric Charge Location in an Atom

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

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.

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

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.

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

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.

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

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.

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.

++–– ++––

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.

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.

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.

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.

–– ++

++––

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.

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.

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)

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

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.

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

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

Charge and Mass of the Atomic Particles

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

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.

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.

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.

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

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.

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 .

Coulomb’s Law

• Solution F23 = ?

• F13 = ?

Coulomb’s Law

• ....Solution

• Now F23 = 9 N and F13 = 11 N

• Is really F3 = F23 + F13 = ?

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.

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