# Lecture 04

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## Lecture 04

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1. Lecture 04 The Electric Field Chapter 22 - HRW Electric Field

2. Physics 2049 News • WebAssign was due today • Another one is posted for Friday • You should be reading chapter 22; The Electric Field. • This is a very important concept. • It is a little “mathy” • There will be a QUIZ on Friday. • Material from chapters 21-22. • Studying Works! Electric Field

3. This is WAR Ming the merciless this guy is MEAN! • You are fighting the enemy on the planet Mongo. • The evil emperor Ming’s forces are behind a strange green haze. • You aim your blaster and fire … but …… Electric Field

4. Nothing Happens! The Green thing is a Force Field! The Force may not be with you …. Electric Field

5. Side View The FORCE FIELD Force Big! |Force| o Position Electric Field

6. Properties of a FORCE FIELD • It is a property of the position in space. • There is a cause but that cause may not be known. • The force on an object is usually proportional to some property of an object which is placed into the field. Electric Field

7. EXAMPLE: The Gravitational Field That We Live In. M m mg Mg Electric Field

8. The gravitational field: g • The gravitational field strength is defined as the Force per unit mass that the field creates on an object • This becomes g=(F/m)=(mg/m)=g • The field strength is a VECTOR. • For this case, the gravitational field is constant. • magnitude=g (9.8 m/s) • direction= down Electric Field

9. Final Comment on Gravitational Field: Even though we know what is causing the force, we really don’t usually think about it. Electric Field

10. Newton’s Law of Gravitation m R Electric Field MEarth

11. The Calculation Electric Field

12. Not quite correct …. Earth and the Moon (in background), seen from space) Electric Field

13. More better … Moon Fmoon m mg FEarth Electric Field MEarth

14. To be more precise … • g is caused by • Earth (MAJOR) • moon (small) • Sun (smaller yet) • Mongo (extremely teeny tiny) • g is therefore a function of position on the Earth and even on the time of the year or day. Electric Field

15. The Electric Field E • In a SIMILAR WAY • We DEFINE the ELECTRIC FIELD STRENGTH AS BEING THE FORCE PER UNIT CHARGE. • Place a charge q at a point in space. • Measure (or sense) the force on the charge – F • Calculate the Electric Field by dividing the Force by the charge, Electric Field

16. Electric Field

17. Electric Field Near a Charge Electric Field

18. Two (+) Charges Electric Field

19. Two Opposite Charges Electric Field

20. A First Calculation Q A Charge r q The spot where we want to know the Electric Field Place a “test charge at the point and measure the Force on it. Electric Field

21. Doing it Q A Charge r F q The spot where we want to know the Electric Field Electric Field

22. General- Electric Field

23. Continuous Charge Distribution Electric Field

24. ymmetry Electric Field

25. Let’s Do it Real Time Concept – Charge per unit length m dq= mds Electric Field

26. The math Why? Electric Field

27. q dEy dE q r x dx L setup A Harder Problem A line of charge m=charge/length Electric Field

28. (standard integral) Electric Field

29. Completing the Math 1/r dependence Electric Field

30. Dare we project this?? • Point Charge goes as 1/r2 • Infinite line of charge goes as 1/r1 • Could it be possible that the field of an infinite plane of charge could go as 1/r0? A constant?? Let's look at it... Electric Field

31. The Geometry Define surface charge density s=charge/unit-area dq=sdA (z2+r2)1/2 dA=2prdr dq=s x dA = 2psrdr Electric Field

32. (z2+r2)1/2 q Electric Field

33. (z2+r2)1/2 Final Result Electric Field

34. Look at the “Field Lines” Electric Field

35. What did we learn in this chapter?? • We introduced the concept of the Electric FIELD. • We may not know what causes the field. (The evil Emperor Ming) • If we know where all the charges are we can CALCULATE E. • E is a VECTOR. • The equation for E is the same as for the force on a charge from Coulomb’s Law but divided by the “q of the test charge”. Electric Field

36. What else did we learn in this chapter? • We introduced continuous distributions of charge rather than individual discrete charges. • Instead of adding the individual charges we must INTEGRATE the (dq)s. • There are three kinds of continuously distributed charges. Electric Field

37. Kinds of continuously distributed charges • Line of charge • m or sometimes l = the charge per unit length. • dq=mds (ds= differential of length along the line) • Area • s = charge per unit area • dq=sdA • dA = dxdy (rectangular coordinates) • dA= 2prdr for elemental ring of charge • Volume • r=charge per unit volume • dq=rdV • dV=dxdydz or 4pr2dr or some other expressions we will look at later. Electric Field

38. The Sphere dq r thk=dr dq=rdV=r x surface area x thickness =r x 4pr2 x dr Electric Field

39. Summary (Note: I left off the unit vectors in the last equation set, but be aware that they should be there.) Electric Field

40. To be remembered … • If the ELECTRIC FIELD at a point is E, then • E=F/q (This is the definition!) • Using some advancedmathematics we can derive from this equation, the fact that: REMEMBER THIS ! Electric Field

41. Example: Electric Field

42. Solution Electric Field

43. q1 = -9q q2=+2q In the Figure, particle 1 of charge q1 = -9.00q and particle 2 of charge q2 = +2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero?[1.89]L(b) Plot the strength of the electric field as a function of position (z). Electric Field

44. Let’s do it backwards… Electric Field

45. EXCEL ETC …. Electric Field

46. ?? alpha=1.89 Electric Field

47. The mystery solved!!! BE CAREFULL! Electric Field

48. In the Figure, the four particles are fixed in place and have charges q1 = q2 = +5e, q3 = +3e, and q4 = -12e. Distance d = 9.0 mm. What is the magnitude of the net electric field at point P due to the particles? Electric Field

49. Electric Field

50. Figure 22-34 shows two charged particles on an x axis, q = -3.20 10-19 C at x = -4.20 m and q = +3.20 10-19 C at x = +4.20 m. (a) What is the magnitude of the net electric field produced at point P at y = -5.60 m?[7.05e-11] N/C(b) What is its direction?[180]° (counterclockwise from the positive x axis) Electric Field