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Understanding Electric Field Concepts and Calculations

Learn about the fundamentals of the Electric Field, including definitions, properties, calculations, and examples. Explore how it relates to charges, forces, and continuous charge distributions. Dive into the math behind Electric Fields.

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Understanding Electric Field Concepts and Calculations

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  1. Lecture 04 Electric Field Electric Field

  2. Physics 2049 News • WebAssign was due today • Another will be there for Monday. • Short week … no quiz unless you want one. • You should be reading chapter 22; The Electric Field. • This is a very important concept. • It is a little “mathy” 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

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