Electric Forces and Electric Fields

1. Chapter 18 Electric Forces and Electric Fields

2. Outline • The origin of Electricity • Charged Objects and the Electric Force • Conductors and Insulators • Charging by Contact and by Induction • Coulomb’s Law • The Electric Field • Electric Field Lines • The Electric Field Inside a Conductor: Shielding • Gauss’s Law • Copiers and Computer Printers • Concepts and Calculations

3. 1- The Origin of Electricity • The electrical nature of matter is inherent in atomic structure: • Electric charge is an intrinsic property of protons and electrons. • A proton has a positive charge, and an electron has a negative charge . • The magnitude of the charge on the proton exactly equals the magnitude of the charge on the electron The proton carries the charge +e The electron carries the charge –e

4. 2- Charged Objects and the Electric Force • Manifestations: • Rubbing a glass rod can deflect a stream of water. • Comb attracting bits of paper. • Upon rubbing, these materials become electrically charged. • Electric charges are transferred. • There are negative and positive electric charges

5. Properties: • Like charges repel each other whereas unlike charges attract each other

6. Negative charges can be transferred between unlike materials. • Electric charge is always conserved • Charge is quantized. Charge = ne with n being a + or – integer e = 1.6 x 10-19 C The SI unit of charge is the Coulomb (C)

7. 3-Insulators and Conductors • Conductors are materials in which the electric charges move freely • Copper, aluminum and silver are good conductors • Insulators are materials in which electric charges do not move freely • Glass and rubber are examples of insulators • The characteristics of semiconductors are between those of insulators and conductors • Silicon and germanium are examples of semiconductors

8. 4-Charging by Contact and by Induction Conductors can be charged by conduction

9. Conductors can be charged by induction

10. Insulators can be polarized by induction

11. 5- Coulomb’s Law The magnitude of F is: Where: Forces are always along the line joining the two charges. For more than 2 charges the superposition principle applies

12. The superposition principle

17. 6- The Electric Field • An electric field is said to exist in the region of space around a charged object. E is a vector whose: • Magnitude (strength) , where F is the force exerted on q0 • Direction is that of the electric force exerted on q0 if q0 is positive.

19. For several charges the superposition principle applies and the electrical field is equal to the vectorial sum of the electric fields produced by each charge

20. The superposition principle

21. 7- Electric Field Lines

22. The electric field vector, E, is tangent to the electric field lines at each point • The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region. • Electric field vectors, E, begin on the positive charge and terminates on the negative charge. • No lines can cross each other.

23. Electric Field Line Patterns • An electric dipole consists of two equal and opposite charges • The high density of lines between the charges indicates the strong electric field in this region

26. 8- The Electric Field Inside a Conductor: Shielding When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium

27. The electric field is zero everywhere inside the conducting material • Consider if this were not true • if there were an electric field inside the conductor, the free charge there would move and there would be a flow of charge • If there were a movement of charge, the conductor would not be in equilibrium 2. Any excess charge on an isolated conductor resides entirely on its surface • A direct result of the 1/r2 repulsion between like charges in Coulomb’s Law • If some excess of charge could be placed inside the conductor, the repulsive forces would push them as far apart as possible, causing them to migrate to the surface

28. Shielding The electric field just outside a charged conductor is perpendicular to the conductor’s surface

29. 9- Gauss’s Law • Electric flux (EA):

30. qis the angle between the vector E and the normal to the surface • In general:

31. Gauss’ Law • Gauss’ Law states that the electric flux through any closed surface is equal to the net charge Q inside the surface divided by εo • εo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2

32. When the area is constructed such that a closed surface is formed, use the convention that flux lines passing into the interior of the volume are negative and those passing out of the interior of the volume are positive

33. Example: The electric field of a charged thin spherical shell A positive charge is spread uniformly over the shell. Find the magnitude of the electric field at any point (a) outside the shell and (b) inside the shell.

35. Outside the shell, the Gaussian surface encloses all of the charge. (b) Inside the shell, the Gaussian surface encloses no charge.

36. Example: The electric field inside a parallel plate capacitor Electric flux through surface 1: Electric flux through surface 2: Electric flux through surface 3: Overall electric flux through Gaussian surface:

37. σ is the charge per unit area