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Chapter 1

Chapter 1. Electricity and Magnetism Dr. Mahmoud Wahdan. The Concept of Electric Charge. Sparks can be produced and lightweight objects attracted when the fossilized resin called amber is rubbed with fur. (Greek Thales)

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Chapter 1

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  1. Chapter 1 Electricity and Magnetism Dr. Mahmoud Wahdan

  2. The Concept of Electric Charge • Sparks can be produced and lightweight objects attracted when the fossilized resin called amber is rubbed with fur. (Greek Thales) • The Greek word for amber is elektron, from which we drive our word electricity. • American Benjamin Franklin: • Electricity  lightning • “positive” and “negative” are two kinds of electrification

  3. Atoms as the Source of Charge • An atom is composed of a tiny positively charged nucleus around which are negatively charged particles called electrons. • Fig. 1.1: atom of carbon • Atoms are electrically neutral. (chemistry) • The quantity of positive charge on the nucleus exactly equals the quantity of total negative charge on electrons about the nucleus. • In the case of the carbon atom, if –e is the charge on each electron, the charge on the nucleus is exactly +6e.

  4. Atoms as the Source of Charge Fig 1.1: A schematic representation of a carbon atom. The negative charges on its six electrons are exactly balanced by the positive nuclear charge. (The nucleus are electrons are much smaller than shown)

  5. Forces Between Charges • Suppose we have positively and negatively charged bodies. • How to examine the forces between charges (Fig. 1.2)

  6. Forces Between Charges (Cont.) Fig. 1.2: In (a) the balls are uncharged. The charged balls in (b), (c ), and (d) show that like charges repel one another while unlike charges attract one another.

  7. Forces Between Charges (Cont.) • Conclusion: • Like charges repel one another: • Two positive charges repel each other, as do two negative charges. • Unlike charges attract one another: • positive charges attract negative charges, and vice versa. • The magnitude of the electric force between two charged objects often exceeds the gravitational attraction between them. • For example: the gravitational force between the two balls in (b), (c ), and (d) is far too small to affect the way they hang).

  8. Insulators and Conductors • There are two basic groups into which substances can be divided according to their electrical properties: conductors and nonconductors (or insulators).* • Insulators: • The electrons of any given atom are bound tightly to that atom and are not free to move through the material. • * A third class of substances, called semiconductors, act as either insulators or conductors depending on temperature and other energy conditions imposed on them.

  9. Insulators and Conductors (Cont.) • If a charged rod is brought close to an insulator, the electrons and nuclei in the atoms of the insulator cannot move under the attraction or repulsion of the rod’s charge. • Conductors: • Substances contain charges that are free to move throughout the material. • Metals are familiar conductors. ebonite

  10. Charging by Conduction and by Induction • There are two general ways of placing charge on a metal object using a second object that is already charged. • Charging by conduction • Charging by induction

  11. Charging by Conduction and by Induction (Cont.) • Charging by conduction • Ex: • Using a negatively charged ebonite rod (hard rubber) to charge a metal ball. • Touching the ball to the rod (Fig. 1.3). • On contact, some of the excess negative charge on the rod moves onto the ball. • This process, shown in Fig. 1.3, is called charging by conduction.

  12. Charging by Conduction and by Induction (Cont.) • Fig. 1.3: When the negatively charged ebonite rod touches the uncharged metal ball, electrons are conducted off the rod onto the ball.

  13. Charging by Conduction and by Induction (Cont.) • Charging by induction • Ex: • Using a negatively charged ebonite rod (hard rubber) to charge a metal ball (Fig. 1.4). • The rod is not touched to the ball at all. • When the rod is brought close to the left side of the ball, some of the electrons in the metal are repelled to the right side of the ball, leaving a positive charge on the left side. • No charge has been added to or subtracted from the ball  electrically neutral.

  14. Charging by Conduction and by Induction (Cont.) • Suppose you touch the ball with your finger. • Because your body is a conductor, charge moves from the ball through your body to the earth. • Thus the nearby negatively charged rod induces negative charge to leave the ball and move to the ground. • We say: the ball is grounded ( ). • After the conducting path to ground is removed, the negative rod can be taken away and the ball will have a positive charge.

  15. Charging by Conduction and by Induction (Cont.) • Fig. 1.4: Charging a metal ball by induction. Note that the rod and the ball never touch, but the finger and ball do. As a result of this process, the rod and ball end up with unlike charges.

  16. Charging by Conduction and by Induction (Cont.) • Comparing Figs. 1.3 and 1.4: • An ebonite rod can charge a metal object negativelyby conducting but it charges the same object positively by induction.

  17. Coulomb’s Law • The mathematical law that describes how like charges repel and unlike charges attract each other was discovered in 1785 by Charles Augustin de Coulomb and is called Coulomb’s law. • Coulomb was able to measure the force between two small charged objects (Fig. 1.5)

  18. Coulomb’s Law (Cont.) • Two balls, small enough to be considered points relative to the distance r between their centers, carry charges +q1 and –q2. • Coulomb concluded that the force on ball 1: F q1q2 / r 2 Fig 1.5: The two unlike charges attract each other with equal forces, even if the charges are unequal in magnitude.

  19. Coulomb’s Law (Cont.) F= constant q1q2 / r 2 (1.1) • If the two charges were either both +ve or both –ve, the magnitude of the force would be the same but the direction would be the reverse of what is shown in Fig. 1.5. • According to Newton’s law of action and reaction, the force on ball 2 must be identical in magnitude but oppositely directed.

  20. Coulomb’s Law (Cont.) • The International System of Units (SI) charge unit is the coulomb (C ). • From (1.1), Coulomb’s law can be written F = kq1q2 / r 2 (1.2) Where: F : newtons r : meters K = 8.9874 x 109 N.m2/C2 9.0 x 109 N.m2/C2

  21. Coulomb’s Law (Cont.) • The constant k is often written as ¼ 0where 0 is called the permittivity of vacuum. 0=8.85 x 10-12 C2 / N.m2 • The fundamental quantity of charge is carried by the electron and proton (e) e =1.60218 x 10-19 C • The proton has a charge of +e, the electron –e.

  22. Coulomb’s Law (Cont.) Example 1.1 A copper penny has a mass of about 3g and contains about 3 x 1022 copper atoms. Suppose two pennies have a fraction of their electrons removed, leaving them each with a net positive charge +q. When one penny is placed on a table, the other will be suspended against its weight by the electric force 2m above the first, as shown in Fig. 1.6. • How large must q be to balance the weight of the penny? • How many electrons must each penny have lost to produce +q? • What fraction of the copper atoms must be missing the electron?

  23. Coulomb’s Law (Cont.) Fig. 1.6: Only a tiny fraction of electrons needs to be removed from a penny to give rise to large electric forces.

  24. Coulomb’s Law (Cont.) Reasoning Part (a) QuestionWhat is the weight of a penny? Answer Weight = mg = (3 x 10-3 kg)(9.8 m/s2) = 0.03 N QuestionWhat is the expression for the electric force on the upper penny? Answer Equation 1.2 where q is the charge on each penny.

  25. Coulomb’s Law (Cont.) QuestionWhat equation determines the charge q? Answer The magnitude of the force F must equal the weight, 0.03 N, so Reasoning Part (b) QuestionOnce q is found, what determines the number of electrons removed? Answer Each electron removed leaves the penny with an excess charge +e. Thus the number of electrons removed is n = q/e.

  26. Coulomb’s Law (Cont.)

  27. Coulomb’s Law (Cont.)

  28. Coulomb’s Law (Cont.) Fig. 1.7: The central charge is attracted to q1 by force F1 and to q3 by force F3.

  29. Coulomb’s Law (Cont.)

  30. Coulomb’s Law (Cont.)

  31. Coulomb’s Law (Cont.)

  32. Coulomb’s Law (Cont.)

  33. Coulomb’s Law (Cont.)

  34. Coulomb’s Law (Cont.) (a) (b) Fig. 1.8: The vector forces acting on the 20 C charge produce the resultant force F shown in (b).

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