ELECTRICITY & MAGNETISM (Fall 2011)

1. ELECTRICITY & MAGNETISM (Fall 2011) LECTURE # 2 BY MOEEN GHIYAS

2. (Chapter 1 – Physical Measurements, Atomic Structure Chapter 22 / 23 – Electric Charge) Fundamentals of Physics by Halliday / Resnick / Walker (6th / 7th Edition) TODAY’S lesson

3. 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

4. Lengths – Some Measured Approximate Values

5. 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

6. Masses – Various Bodies (Approximate Values)

7. Time – Approximate Values of Some Time Intervals Age of Universe = in years? = 5 x 1017 / (60x60x24x365) = 158 billion years

8. 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

9. The Greek Alphabets

10. 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.

11. 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.

12. 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.

13. Atomic Structure

14. 3 Major Parts Of An Atom • Proton • Neutron • Electron

15. Electric Charge Location in an Atom

16. 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

17. 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.

18. 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

19. 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.

20. 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

21. 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.

22. 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

23. 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.

24. 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. – – + +

25. 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.

26. 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.

27. 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.

28. 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. – + – +

29. 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.

30. 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.

31. 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)

32. 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? • +10e • -6e • 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

33. 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.

34. 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

35. 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

36. Charge and Mass of the Atomic Particles

37. 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

38. 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.

39. 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.

40. 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.

41. 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

42. 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.

43. 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 .

44. Coulomb’s Law • Solution F23 = ? • F13 = ?

45. Coulomb’s Law • ....Solution • Now F23 = 9 N and F13 = 11 N • Is really F3 = F23 + F13 = ?

46. 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.

47. 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