Electricity

1. Electricity

2. Static Electricity • Charge comes in two forms, which Ben Franklin designated as positive (+) and negative (-). • Charge is quantized. • The smallest possible stable charge, designated as e, is the magnitude of the charge on 1 electron or 1 proton. • A proton has charge of e, and an electron has charge of -e. • e is referred to as the “elementary” charge. • e = 1.602 x 10-19 coulombs. • The coulomb is the SI unit of charge.

3. Sample Problem • A certain static discharge delivers -0.5 coulombs of electrical charge. How many electrons are in this discharge? • q = n e • n = q/e • n = (-0.5 C) / (-1.602 x 10-19 C) • n = 3,121,098,626,716,604,245 • OR 3.12 x 10 18

4. Sample Problem • 1. How much positive charge resides in two moles of hydrogen gas (H2)? • 2. How much negative charge? • 3. How much net charge?

5. Sample Problem • The total charge of a system composed of 1800 particles, all of which are protons or electrons, is 31x10-18 C. • How many protons are in the system? • How many electrons are in the system?

6. Coulomb’s Law and Electrical Force

7. Demo #1 • 1. Demonstrate how you can pick up the tissue without touching it in any way with your body. • 2. What is occurring on the atomic level that lets you do this?

8. The atom • The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction. • The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without too much difficulty.

9. So… • You charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?

10. The Electroscope • The electroscope is • Made from a metal • Or other conductor, • And may be contained • Within a flask. • The vanes are free • to move.

11. Demo #2 • Rub the plastic rod with the fur. Bring the rod toward the pole of the electroscope. What happens to the vanes? • Explain your observations.

12. Demo #3 • Rub the glass rod with the silk. Bring the rod toward the pole of the electroscope. What happens to the vanes? • Explain what you observe.

13. Demo #4 1. What happens when you touch the electroscope with the glass rod?

14. Electric Force • Charges exert forces on each other. • Like charges (two positives or two negatives) repel each other resulting in a repulsive force. • Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.

15. Coulomb’s Law - form 1 • Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them. • Coulomb’s law applies directly only to spherically symmetric charges.

16. Coulomb’s Law - form 2

17. Spherically Symmetric Forces Newton’s Law of Gravity FG = Gm1m2 r2 Coulomb’s Law FE = kq1q2 r2

18. Sample Problem

19. Sample Problem

20. Superposition • Electrical force, like all forces, is a vector quantity. • If a charge is subjected to forces from more than one other charge, vector addition must be performed. • Vector addition to find the resultant vector is sometimes called superposition.

23. The Electric Field

25. Gravitational Fields • S F = ma • GmEmm = ma • (2rE) 2 • a = G m E • 4rE2

26. The Electric Field

27. Why use fields? • Forces exist only when two or more particles are present. • Fields exist even if no force is present. • The field of one particle only can be calculated.

28. Field around a + charge **The arrows in a field are not vectors, they are “lines of force”. **The lines of force indicate the direction of the force on a positive charge placed in the field. **Negative charges experience a force in the opposite direction.

29. Field around a - charge

30. Field between charged plates

31. Field vectors from field lines • The electric field at a given point is not the field line itself, but can be determined from the field line. • The electric field vector is always tangent to the line of force at that point. • Vectors of any kind are never curved!

32. Field Lines and Pathof Moving Charge • The electric field lines do not represent the path a test charge would travel. • The electric field lines represent the direction of the electric force on a test particle placed in the field.

33. Field Vectors from Field Lines

34. Force from an Electric Field • The force on a charged particle placed in an electric field is easily calculated. • F = Eq • F: Force (N) • E: Electric Field (N/C) • q: Charge (C)

35. Sample Problem

36. Sample Problem

37. Sample Problem • A proton traveling at 440 m/s in the +x direction enters an electric field of magnitude of 5400 N/C directed in the +y direction. Find the acceleration.

38. For Spherical Electric Fields • The electric Field surrounding a point charge or a spherical charge can be calculated by: E = k q / r2 where • E: Electric Field (N/C) • k: 8.99 x 109 N m2 / C2 • q: Charge (C) • r: distance from center of charge q (m) • Remember that k = 1/4peo

39. Principle of Superposition • When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges. • Again, as with force vectors, this is referred to as superposition.

40. Keep in mind… • Electric field lines are NOT vectors, but may be used to derive the direction of electric field vectors at given points. • The resulting vector gives the direction of the electric force on a positive charge placed in the field.

41. Sample Problem • A particle bearing -5.0 mC is placed at -2.0 cm and a particle bearing 5.0 mC is placed at 2.0 cm. What is the field at the origin?

42. Sample Problem

43. Sample Problem

44. Electric Potential Energy • The energy contained in a configuration of charges. • Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable. • Unit: Joule

45. Electric Potential Energy • increases when charges are brought into less favorable configurations. DU>0

46. Electric Potential Energy • decreases when charges are brought into more favorable configurations. DU<0

47. Electric Potential Energy

48. Work and Charge

49. Work and Charge

50. Electric Potential • Electric potential is hard to understand, but each to measure. • We commonly call it “voltage”, and its unit is the Volt. • 1 V = 1 J / C • Electric potential is easily related to both the electric potential energy and to the electric field.