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Lecture 1 Charge and Coulomb’s Law

Lecture 1 Charge and Coulomb’s Law. Ch (25) in the book of Randall D. Knight,  Physics for Scientists and Engineers , 3rd edition. Please join Facebook group EM Fields_1st year_Zag_Inst Use your real name on your Facebook profile. The History of Electricity.

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Lecture 1 Charge and Coulomb’s Law

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  1. Lecture 1Charge and Coulomb’s Law Ch (25) in the book of Randall D. Knight, Physics for Scientists and Engineers, 3rd edition. Please join Facebook group EM Fields_1st year_Zag_Inst Use your real name on your Facebook profile

  2. The History of Electricity ElectricÞelektron = Greek word for amber “Rub amber with wool, and it will pick up bits of wood, feathers, straw …” Thales of Miletus (640-546 BC) About 1736, Charles Francois du Fay (1698-1739) learned that rubbing glass and rubbing resinous substances (e.g., amber) seemed to produce charges of different kinds. He found that two charges of the same kind repelled each other, while two of unlike kinds attracted. He suggested that electricity might exist as two distinctly different types, which he named “vitreous” and “resinous” electricity. William Watson (1715-1790) suggested in 1746 that electricity was one “fluid”. One of the two kind of electricity proposed by Du Fay could be an excess (+) of this fluid and the other a deficiency of it (-). Flow from + to - could account for electrical discharge. Benjamin Franklin (1706-1790) adopted and popularized Watson's “one fluid” theory and chose vitreous electricity to be the positive type (thereby giving electrons a negative charge). Franklin’s great reputation won universal acceptance for this view.

  3. Charging Experiments (1) Observations: No force is observed between un-rubbed rods. Plastic rods rubbed with wool repel each other. Two glass rods rubbed with silk also repel each other. Glass rod rubbed with silk attracts plastic rod rubbed with wool. At increased distance, forces are decreased.

  4. Charging Experiments (2) 3 2 1 • More Observations: • A (charged) plastic/glass rod rubbed with wool attracts small pieces of paper. • A (charged) plastic/glass rods rubbed with wool is attracted to an un-rubbed (neutral) plastic rod. • A plastic rod rubbed with wood is attracted to the wool, repelled by the silk. • No charged (rubbed) object attracts both the charged plastic rod and the charged glass rod. 4

  5. Charging Experiments (3) 2 1 3 • Even More Observations: • The charge from a plastic rod rubbed with wool can be transferred to a metal sphere. • After the transfer, the plastic rod does not attract paper. • A 2ndmetal sphere connected by a metal rod acquires the rod’s charge. • A 2nd metal sphere connected by a plastic rod does not acquire the rod’s charge. 4

  6. Electric Charge and Atoms An atom with atomic number Z consists of a small but massive nucleus of charge +Ze, surrounded by a cloud of Z electrons, each with much less mass and with a charge of -e. The atom has a diameter of about 10-10 m (0.1 nm), while the atomic nucleus has a diameter of about 5x10-15 m (5 fm). All atoms, heavy or light, are about the same size, but the mass varies from 1 to ~250. The nucleus contains Zprotons with charge +e and N neutrons with charge 0. The atomic mass number of the atom is A = Z+N. Charge: q = Npe-Nee = (Np-Ne)e ; for neutral atoms (q=0), Np=Ne=Z

  7. Positive and Negative Ions Atoms can have a net charge ifNp¹Ne, whereNp=Zis the number of protons andNeis the number of electrons in the atom. If a neutral atom loses one electron, it will have a net positivecharge ofq=+e because Np-Ne=+1. If a neutral atom gainsone electron, it will have a net negativecharge of q=-e because Np-Ne=-1.

  8. Charging by Friction Friction causes the breaking of molecular bonds, and can result in a separation of charges in a formerly neutral molecule, creating a positive and a negative molecular ion. Rubbing a plastic rod with wool or a glass rod with silk produces such charge separation effects.

  9. Conservation of Charge Electrical charge can be neither created or destroyed. It can be separated and moved around, but the net charge of an isolated system must remain constant.qinitial = qfinal Example: A plastic rod is rubbed with wool, each initially neutral. Thenqwool= - qrod.

  10. Insulators and Conductors (1) If a conductor is charged, all of the charge must reside on the outer surface (and none in the interior.) If an insulator is charged, the charge may (or may not) reside in the interior.

  11. Insulators and Conductors (2) In insulators, the electrons are tightly bound in the atoms and are not free to move around. When insulators are charged, e.g. by friction, patches of molecular ions are created on the surface, but these patches are immobile. In solid metal conductors, the outer (valence) electrons of the atoms are only weakly bound and are free to move around in the solid. The conductor as a whole may be electrically neutral, but the electrons are rather like an electrically charged liquid, a “sea” of electrons within the material. Electrons are the “charge carriers”. There are other forms of conduction (in ionic liquids, etc.) in which the charge carriers are not electrons.

  12. Charging an Insulator

  13. Charging a Conductor Conductors cannot be charged by friction. However, charge can be transferred to a conductor by contact with a charged object. The charges arriving at the conductor stay on the outer surface and distribute themselves over that surface so that they are as far away as possible from the repulsive forces of the other charges.

  14. The Electroscope The ElectroscopeMeasuring instrument that detects electric charge; two gold leaves diverge owing to repulsion of charges with like sign

  15. Charging an Electroscope The angleof deflection of the leaves provides a rough indication of the amount of charge that has been deposited on the electroscope.

  16. Discharging a Charged Object The human body, composed mainly of salty water, is a moderately good conductor. Therefore, a person touching a charged object will normally discharge the object. • Any excess charge that was initially confined to the metal can now spread over the larger metal + human conductor. Where the charge goes next depends on the degree to which the person is insulated from ground (e.g., by rubber shoe soles).

  17. Charge Polarization

  18. Induced Charge By using charge polarization, it is possible to induce charge on an electrically neutral object. Example: Bring a charged rod near (but not touching) an electroscope and observe the effect on the leaves. -- - - - - - - + + + + + +

  19. Charges and Forces

  20. The Electric Dipole Experiment: Bring a positive charge near a neutral atom.

  21. Dipoles and Forces (1)

  22. Dipoles and Forces (2)

  23. Charging by Induction Induction: Charging an object with only neutral contact.

  24. Coulomb’s Law Like charges repel. Charles Augustine de Coulomb (1736-1806). Opposite charges attract. ( Magnitude of force ) Coulomb’s Law:

  25. Units of Charge Coulomb’s Law, written two ways. (Note that in Newton’s law of gravitation, G, which plays a role similar to K, has the valueG = 6.67 ´10-11 N m2/kg2.)

  26. Using Coulomb’s Law • Coulomb’s Law applies only to point charges. • (This is particularly important because charge are free to move around on conductors.) • Strictly speaking, Coulomb’s Law applies only to electrostatics (non-moving charges). • (However, it is usually OK provided v<<c). • Electrostatic forces can be superposed. • Linear superposition !!!!

  27. Example(1): Sum of Two Forces Two +10 nC charged particles are 2 cm apart on the x axis. (1) What is the net force on a +1.0 nC particle midway between them? (2) What is the net force if the charged particle on the right is replaced by a -10 nC charge? Solution: (1) -9 9 (2)

  28. Example(2): Point of Zero Force Two positively charged particles q1 and q2=3q1 are placed 10.0 cm apart. Where (other than infinity) could another charge q3 be placed so as to experience no net force? Solution: • We need force vectors to be co-linear, so location must be on x axis. • We need force vectors to be in opposite directions, so location must be between 0 and d. • We need force vectors equal in magnitude, so F=Kq1q3/x2=Kq2q3/(d-x)2. Therefore,(d-x)2=3x2orx=d/(1±√3) = 10 cm/(1±1.732); x+=10.0 cm/2.732 = 3.66 cm; x-=10.0 cm/-0.732=-13.66 cm, which does not satisfy the 2nd criterion. so x+= 3.66 cm is the only solution.

  29. Example(3): Three Charges (1) Three charges with q1 = -50 nC, q2 = +50 nC, and q3 = +30 nC, are placed at the corners of a 10 cm x 5 cm rectangle as shown. What is the net force on q3 due to the other two charges? Solution:

  30. Example(3): Three Charges (2) Cos q Sin q Fnet

  31. Example(4): Lifting a Glass Bead A small plastic sphere is charged to -10 nC. It is held 1.0 cm above a small glass bead that rests on a table. The bead has a mass of 15 mg and a charge of +10 nC. Will the glass bead “leap up” to the plastic sphere? Solution: Therefore, F1 on 2 exceeds w by a factor of 60. Therefore, the glass bead should indeed leap upward. (Note that we have neglected electrical forces between the bead and table, which could be significant.)

  32. End of Lecture 1 • Before the next lecture, read Knight, Chapters 25.5 through 26.1

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