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# ELECTRIC FORCES AND ELECTRIC FIELDS

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1. ELECTRIC FORCES AND ELECTRIC FIELDS Classwork problems Coulomb’s law 1,3,8,9,10,11,13 Electric Fields 19,21,23,25,27-29 Field Lines 30,32-35 Van deGraff 36,39 Gauss’s law 41,45,47

2. OBJECTIVES • After studying the material of this chapter, the student should be able to: • 1. State from memory the magnitude and sign of the charge on an electron and proton and also state the mass of each particle. • 2. Apply Coulomb's law to determine the magnitude of the electrical force between point charges separated by a distance r and state whether the force will be one of attraction or repulsion. • 3. State from memory the law of conservation of charge. • 4. Distinguish between an insulator, a conductor and a semi-conductor and give examples of each.

3. OBJECTIVES • 5. Explain the concept of electric field and determine the resultant electric field at a point some distance from two or more point charges. • 6. Determine the magnitude and direction of the electric force on a charged particle placed in an electric field. • 7. Sketch the electric field pattern in the region between charged objects. • 8. Use Gauss's law to determine the magnitude of the electric field in problems where static electric charge is distributed on a surface which is simple and symmetrical. (Not at this time!)

4. KEY TERMS AND PHRASES static electricity conductor electric charge semiconductor positive charge induced charge negative charge charging by contact law of conservation of charge Coulomb's law electron dielectric(no) proton dielectric constant(no) e permittivity of free space(no) neutron electric field insulator electric field pattern lines of force

5. CONCEPTS AND EQUATIONS ELECTRIC CHARGE • There are two types of ELECTRIC CHARGE, arbitrarily called POSITIVE and NEGATIVE • Rubbing certain electrically neutral objects together (e.g., a glass rod and a silk cloth) tends to cause the electric charges to separate. In the case of the glass and silk, the glass rod loses negative charge and becomes positively charged while the silk cloth gains negative charge and therefore becomes negatively charged. After separation, the negative charges and positive charges are found to attract one another.

6. ELECTRIC CHARGE • If the glass rod is suspended from a string and a second positively charged glass rod is brought near, a force of electrical repulsion results. Negatively charged objects also exert a repulsive force on one another. These results can be summarized as follows: UNLIKE CHARGES ATTRACT, LIKE CHARGES REPEL

7. CONSERVATION OF ELECTRIC CHARGE • In the process of rubbing two solid objects together, electrical charges are NOT created. Instead, both objects contain both positive and negative charges. During the rubbing process, the negative charge is transferred from one object to the other and this leaves one object with an excess of positive charge and the other with an excess of negative charge. The quantity of excess charge on each object is exactly the same.

8. CONSERVATION OF ELECTRIC CHARGE • This is summarized by the LAW OF CONSERVATION OF ELECTRIC CHARGE: the net amount of electric charge produced in any process is zero. Another way of saying this is that in any process electric charge CANNOT be created or destroyed, however, it can be transferred from one object to another.

9. Subatomic Particles • During the past century, the negative charges have been shown to be carried by particles which are now called ELECTRONS while the positive charge carriers are known as PROTONS. • The SI unit of charge is the coulomb (C). The amount of charge transferred when objects like glass or silk are rubbed together is in the order of microcoulombs ( C). • 1 C = 6.25 x 1018 electrons or protons and I C = 10-6 C.The charge carried by the electron is represented by the symbol -e, and the charge carried by the proton is +e. e = 1.6 x 10-19 coulomb • The mass of an electron is 9. II X 10-31 kg while mass of a proton is 1.672 x10-27 kg. • A third particle, which carries no electrical charge, is the NEUTRON. The neutron has a mass of 1.675 x 10-27 kg.

10. Experiments performed early in this century have led to the conclusion that protons and neutrons are confined to the nucleus of the atom while the electrons exist outside of the nucleus. When solids are rubbed together, it is the electrons which are transferred from one object to the other. The positive charges, which are located in the nucleus, do not move.You may encounter discrepancies to this theory.

11. INSULATORS, SEMICONDUCTORS AND CONDUCTORS • An INSULATOR is a material in which the electrons are tightly held by the nucleus and are not free to move through the material. There is no such thing as a perfect insulator, however, examples of good insulators include substances such as glass, rubber, plastic and dry wood.

12. INSULATORS, SEMICONDUCTORS AND CONDUCTORS • A CONDUCTOR is a material through which electrons are free to move through the material. Just as in the case of the insulators, there is no such thing as a perfect conductor. Examples of good conductors include metals, such as silver, copper, gold and mercury.

13. INSULATORS, SEMICONDUCTORS AND CONDUCTORS • A few materials, such as silicon, germanium and carbon, are called SEMICONDUCTORS. At ordinary temperatures, there are a few free electrons and the material is a poor conductor of electricity. As the temperature rises, electrons break free and move through the material. As a result, the ability of a semiconducting material to conduct improves with temperature.

14. CHARGING BY INDUCTION • If a negatively charged rod is brought near an uncharged electrical conductor the negative charges in the conductor travel to the far end of the conductor (see diagram).

15. CHARGING BY INDUCTION • The positive charges are not free to move and a charge is temporarily INDUCED at the two ends of the conductor. Overall, the conductor is still electrically neutral and if the rod is removed a re-distribution of the negative charge would occur.

16. CHARGING BY INDUCTION • If the metal conductor is touched by a person's finger or a wire connected to ground, it is said to be "grounded" . The negative charges would flow from the conductor to ground. If the ground is removed and then the rod is removed, a permanent positive charge would be left on the conductor. The electrons would move until the excess positive charge was uniformly distributed over the conductor.

17. CHARGING BY CONTACT • If the rod touches the metal conductor, some of the negative charges on the rod transfer to the metal. This charge distributes uniformly over the metal. The metal has been charged by CONTACT and a permanent charge remains when the rod is removed.

18. Coulomb’s Law

19. COULOMB'S LAW • COULOMB'S LAW states that two point charges exert a force (F) on one another that is directly proportional to the product of the magnitudes of the charges (Q) and inversely proportional to the square of the distance (r) between their centers. The formula relating the force to the charges and the distance is

20. COULOMB'S LAW • In the case of objects in which the electric charge is distributed in such a way that they can be considered to act like "point" charges, e.g., small metal spheres with uniform charge distribution,the distance r is measured from the center of one object to the center of the second object.The value of k given above is for two point charges separated by a distance (r) in a vacuum and to a good approximation dry air. The constant may also be expressed in terms of the permittivity of free space

21. COULOMB'S LAW • The proportionality constant (k) can only be used if the medium which separates the charges is a vacuum. If the region between the point charges is not a vacuum then the value of the proportionality constant to be used is determined by dividing k by the DIELECTRIC CONSTANT (K). For a vacuum (& dry air) K = 1, for distilled water K = 80, and for wax paper K = 2.25 and You can ignore the BIG K for 99.99% of your problems

22. Solving Problems involving Coulomb’s Law • The following is an outline of the steps to be followed in attempting to solve the type of problems found in this chapter. • For problems involving Coulomb's law: • 1. Complete a data table listing the charge on each object and the distance between the objects. If more than two charged objects are given, draw a diagram showing the position of each object. • 2. If the objects touch then charge transfer occurs and the law of conservation of charge must be applied to determine the charge on each object. • 3. If more than two charges are given it may be necessary to use the methods of vector algebra discussed in Chapter 2 to solve the problem. • 4. Apply Coulomb's law and solve the problem.

23. ELECTRIC FIELD • If an electric charge experiences an electric force at a particular point in space, it is in the presence of an ELECTRIC FIELD. The magnitude of the electric field (E) at any point in space can be determined by the ratio of the force (F) exerted on a test charge placed at the point to the magnitude of the charge on the test particle (q). • E = F/q The units of electric field are Newton/coulomb

24. Gravity and Electric Fields g=F/m E=F/q

25. Gravity and Electric Fields F=GMm/r2 g=F/m g= GM/r2 F=kQq/r2 E=F/q E=kQ/r2

26. ELECTRIC FIELD • Electric field is a vector quantity, the direction of the vector is in the same direction as the direction of the force vector if the test charge is positive, and directed opposite from the force vector if the test charge is negative. For a single point charge (Q) the electric field a distance (r) from the charge is given by E = k Q/r2

27. Electric Field Lines • In order to visualize the path taken by a charged particle placed in an electric field, ELECTRIC FIELD LINES, also known as LINES OF FORCE, are drawn. The following diagrams represent the electric field patterns for certain arrangements of charge.

28. Rules For drawing Electric Field Lines • The lines must begin on positive charges and terminate on negative charges, or at infinity in the case of excess charge • The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. • No two field lines can cross

29. Electric Field for two equal and opposite point charges

30. Electric Field for two positive charges

31. Electric Field for two unequal and opposite charges

32. Electric Field Lines • Since a POSITIVE TEST CHARGE is arbitrarily chosen to analyze the field, electric field lines are drawn away from an object with the excess of positive charge and toward an object with an excess of negative charge. In diagrams c, d and e the electric field lines start on the positive charge and terminate on the negative charge.

33. Electric Field Lines • The electric field is strongest in regions where the lines are close together and weak where the lines are further apart. Thus, in diagrams (a) and (b), the field is strongest close to the point charges.

34. Electric Field Lines • In diagram (c) the field weakens as the lines diverge as they leave the positive charge and strengthens as the lines converge on the negative charge. In diagram (e), two parallel plates of opposite charge produce an electric field where the lines are parallel near the center of the plates. In this region the electric field is uniform and E is constant in magnitude and directions start on the positive charge and terminate on the negative charge.

35. Coulomb's law can be used to predict that the electric field inside a closed conductor is zero. An example of a closed conductor is a hollow metal sphere which contains an excess of static electric charge. The charge on the conductor tends to reside on its outer surface. Inside the conductor, the electric field is zero. Outside the conductor, the electric field is not zero and the electric field lines are drawn perpendicular to the surface.