electrical forces, magnetic forces, action-at-a-distance Fields

1. electrical forces,magnetic forces,action-at-a-distanceFields Mico-world Macro-world Lecture 8 + -

2. Benjamin Franklin

3. Ben Franklin Matter is filled with a mysterious Fluid-like substance called “electricity.” When an object has its “normal amount” of electricity, it is electrically “neutral” And doesn’t feel electrical forces. When an object has more than its normal amount of electricity, it is “positively charged.” When it has less than its normal amount it is “negatively charged.” Charged objects feel electrical forces.

4. Friction can move “electricity” from one object to another Franklin hypothesized that rubbing a comb through hair moved some “electricity” from the comb to the hair Comb has an “electricity” deficit & thus becomes negatively charged _ _ _ + Hair has a surplus & becomes positively charged + _ + +

5. Opposite charges attract

6. Like-sign charges repel _ _

7. Modern picture of “electricity” Negatively charged electrons orbit around a positively charged nucleus _ _ + + + Electrical attraction between minus electrons & plus nucleus keeps electrons in orbit _ _ + + _ _

8. Positive Ion An atom with one or more electrons removed _ _ + + + _ _ _ + + _ ”net” charge is positive

9. “electricity” flow “electricity” doesn’t flow from comb to hair, some electrons from hair atoms get stuck on the comb Comb has an excess of of electrons & is thus negatively charged _ _ _ + The removal of each electron leaves a positive ions in the hair + _ + +

11. Atomic electrons play the role of“fluid-like electricity” _ _ + + + _ _ + + _ _

12. positive ion (fixed in crystal) + ElectricalConductors Conduction electron free to move around _ _ _ _ _ _ _ _ _ _ + + + + + + + + + _ _ _ _ _ _ _ _ _ _ + + + + + + + + + _ _ _ _ _ _ _ _ + + + + + + + + + _ _ _ _ _ _ _ _ _ + + + + + + + + + _ _ _ _ _ _ _ _ _ + + + + + + + + +

13. Charging by induction

14. Charging by induction (2)

15. Electroscope

16. Electrical Force Charles Coulomb 1736-1806

17. Coulomb’s Law The electrical force between two charged objects is proportional to the charge of each object and inversely proportional to the square of the distance between them.

18. Coulomb’s law q2 q1 r Fc q1 proportional to the charge of each object Fc q2 Proportionality constant: Inversely proportional to the square of the distance between them 1 r2 Fc “Coulomb’s Constant” q1q2 r2 q1q2 r2 combine: Fc Fc= k

19. Units & Coulomb’s constant Unit of charge = “Coulomb”(C) q1q2 r2 Fc= k Unit of distance = m k = 9.0x109Nm2/C2 This is a big number

20. Hydrogen atom electron qe = -1.6x10 –19 C qp = +1.6x10 –19 C qeqp r2 Fc= k 5x10–11 m (1.6x10-19C)2 (5x10-11m)2 =9x109Nm2/C2 proton =9.2x10-8N

21. Gravitational force in an atom electron me = 9.1x10 –31 kg 5x10–11 m mp = 1.7x10 –27 kg memp r2 proton FN= G 9.1x10-31kgx1.7x10-27kg (5x10-11m)2 =6.7x10-11Nm2/kg2 =4.1x10-47N

22. Electrical vs gravitation at atomic scales FC=9.2x10-8N _ FN=4.1x10-47N 5x10–11 m FC9.2x10-8N FN 4.1x10-47N + = = 2.2x10+39 Electrical force is >1039x the gravitational force!! Fc = 22,000,000,000,000,000,000,000,000,000,000,000,000,000 x FN

23. Magnetismanother “invisible” force

24. N-poles & S-poles S N Unlike poles attract N S

25. N-poles & S-poles S N like poles repel S N

26. N-poles & S-poles can never be isolated S N Break a magnet into two pieces: S N S N A new N-pole & S-pole are formed

27. Compass needles If left to its own accord, the N-pole of a magnet will try to point towards the North

28. The Earth is a magnet Earth’s geographic North pole is a Magnetic S-pole North Pole S N South Pole geographic South pole is a magnetic N-pole

29. Action at a Distance + -

30. q2 M2 q1 M1 Coulomb’s law r All possible distances! q1q2 r2 Fc= k Newton’s law of Gravitation M1M2 r2 FN= G

31. Moon-earth MMME r2 FN=G How does the Moon know that the Earth is where it is (& what ME is)?

32. Electroscope How do the electrons in the foil know that someone is moving a charged object up here? & that it’s negatively charged? & how much it is charged by?

33. Ball on an empty trampoline surface The ball feels no net force

34. Ball on a “loaded” trampoline surface The ball is “attracted” to the girl’s force

35. Luminiferous aether & E-Fields +

36. Faraday’s method for computingE fields Ftest=coulomb force on test charge Ftest E = Ftest/qtest x + Imaginary small positive “test” charge qtest +

37. Example + +

38. E-field from 2 plus charges + +

39. E-field from 2 plus charges

40. E-Field is the dir of force on + charge + -

41. E-Field for opposite charges

42. Better picture + -

43. Rules E-field lines start on + charges and end on - charges Direction of E-field lines = direction of force on a + charge placed at that point (opposite for – charge) Where E-field lines are close together, the E field is large; where they are far apart, the E-field is small. The bigger the charge, the more E-field lines start (or stop) on it. E-field lines never cross

44. Magnetic Fields B-field is in the direction of the net force Imagine a small N-pole is placed at the point x N Determine the magnetic force on the imaginary N-pole S N

45. B-field from a bar magnet S N

46. Rules S N B-field lines come out of N-poles & go into S-poles B-field lines never end Density of B-field strength of the field The stronger the pole, the more B-field exit (or enter)

47. Arrays of magnets

48. ,arrays of magnets

49. Earth’s magnetic field

50. Which ones are N? Which are S?