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Chapter 26

Chapter 26. Electric Field. Electric Field. New long range interaction. A creates field in space changes the environment. B interacts with field. Procedure. Place test charge Find force remove test charge. Simulation: Electric Field. Understanding Fields (in general).

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Chapter 26

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  1. Chapter 26 Electric Field Phys 133

  2. Electric Field New long range interaction A creates field in space changes the environment B interacts with field Phys 133

  3. Procedure • Place test charge • Find force • remove test charge Phys 133

  4. Simulation: Electric Field Phys 133

  5. Understanding Fields (in general) Vector field worksheet (field at tail, relative lengths) Phys 133

  6. Vector field worksheet (cont.) Phys 133

  7. Vector field worksheet (ans) Phys 133

  8. Electric Field: point charge Positive point charge Negative point charge Radial from source, depends on distance Phys 133

  9. Defined or Electric Field (multiple charges) Net force at some point is sum of the forces due to all objects around Therefore, Phys 133

  10. Do workbook 26.5ac, 7adf Phys 133

  11. Electric field of a dipole along the y-axis… Phys 133

  12. Electric field of a dipole along the y-axis… Phys 133

  13. Electric field of a dipole along the y-axis What is the electric field of a dipole for y >> d? Phys 133

  14. Two ways to describe the same thing Vector Field and Field Lines Dipole with +/- Vector field Field lines Phys 133

  15. More Vector Field and Field Lines Dipole with +/+ Vector field Field lines Phys 133

  16. Electric Field lines Rank the electric field strength in order from largest to smallest. A: E1 < E2 < E3 = E4 B: E3 = E4 < E2 < E1 C: E2 = E3 < E4 < E1 D: E1 < E4 < E2 = E3 Phys 133

  17. Electric Field of a “blob” Phys 133

  18. Charge Density Charge Q is spread uniformly on a rectangle of sides a and b. a) What is the surface charge density? b) The original rectangle, #1, is then broken into two smaller rectangles, #2 and #3. Compare the surface charge densities, 1, 2, 3. and the charges Q1, Q2, Q3. Phys 133

  19. Charge Density ans Charge Q is spread uniformly on a rectangle of sides a and b. a) What is the surface charge density? b) The original rectangle, #1, is then broken into two smaller rectangles, #2 and #3. Compare the surface charge densities, 1, 2, 3. Charge is uniformly spread over rectangle. Piece #2 has a 1/3 the area, so 1/3 the charge. Phys 133

  20. (i)th bit of charge Electric Field (continuous distribution) P Phys 133

  21. Strategy  Draw a picture, pick a coordinate system.  Identify, P, the place in space you want the field. • Pick a generic (no special points) chunk of charge DQ for which you know the field.  Determine the components of (Ex, Ey, …) at P due to chunk expressed in terms of variables (x, y, …r, q…). • Express the charge DQin terms of charge density and infinitesimal variable(s) (dz, dq…) Express all quantities (angles, distances, etc.) in terms of coordinates. Add up contributions, sum becomes definite integral with limits corresponding to charge. • Evaluate integral and simplify result as much as possible. Phys 133

  22. Problem A thin rod of length L and charge Q. Find components of the electric field vector along the dotted line. Phys 133

  23. Problem ans Draw a picture, pick a coordinate system. Identify, P, the place in space you want the field. Pick a generic chunk of charge DQ. Determine the components of (Ex, Ey, …) at P due to chunk expressed in terms of variables (x, y, …r, q…). Express the charge DQ in terms of charge density and infinitesimal variable(s) (dz, dq…) Express all quantities (angles, distances, etc.) in terms of coordinates. y ith x P x Phys 133

  24. Problem ans x Add up contributions, sum becomes definite integral with limits corresponding to charge. Phys 133

  25. Problem ans y Add up contributions, sum becomes definite integral with limits corresponding to charge. Phys 133

  26. Problem ans complete Phys 133

  27. Problem 26.49 A plastic rod with linear charge density  is bent into a quarter circle. Find the electric field at the origin. Write expressions for x and y components of field due to a small piece at angle . Write integrals for the components of total field. Evaluate, find Phys 133

  28. Problem 26.49 ans (i)th bit of charge Phys 133

  29. Field of quarter circle of charge Phys 133

  30. Other charge geometries • Line • Hoop • Disk (from hoops) • Plane (from disk) Phys 133

  31. Field of line (infinite) Points directly away, decrease with distance Phys 133

  32. Field of hoop, along axis Phys 133

  33. Field of disk, along axis Phys 133

  34. Field of plane (“infinite”) perpendicular to the plane Phys 133

  35. Plane from lots of lines (perpendicular to page) Straighten up, no distance dependence Phys 133

  36. Parallel-plate Capacitor • Net charge is zero • Charge lost from +Q side ends up on -Q side Phys 133

  37. Find the electric field inside capacitor Phys 133

  38. Phys 133

  39. Charges in an Electric Field Electric Field (due to charges; we can calculate) Charge in Electric Field (experiences a force) Phys 133

  40. Do Workbook 26.28 & 31 Phys 133

  41. Problem 26.52 A proton traveling at a speed of 1.0x106 m/s enters the gap between the plates of a 2.0-cm wide parallel plate capacitor. The plates have a surface charge density of +/- 1.0x10-6 C/m2. How far is the proton deflected when reaching far end of capacitor? (Ans: 2.2 mm) e=1.6 x 10-19C; mp=1.67 x 10-27kg; o=8.85 x10-12C2/N-m2 Phys 133

  42. Dipole in an Electric Field Phys 133

  43. Phys 133

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