1. Chapter 23
Electric Field
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2. Electric Field New long range interaction A creates field in space
changes the environment
B interacts with field
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3. Procedure
Place test charge
Find force
remove test charge
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4. Simulation: Electric Field
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5. Understanding Fields (in general)
Vector field worksheet (field at tail, relative lengths)
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6. Vector field worksheet (cont.)
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7. Vector field worksheet (ans)
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8. Electric Field: point charge
Positive point charge
Negative point charge
Radial from source, depends on distance
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9. Electric Field (multiple charges)
Net force at some point is sum of the forces due to all objects around
Defined
Therefore, or
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10. What is the electric field direction at each of the dots?
Which electric field is larger, E1 or E2?
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11. Electric field of a dipole along the y-axis…
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12. Electric field of a dipole along the y-axis…
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13. Electric field of a dipole along the y-axis
What is the electric field of a dipole for y >> d?
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14. Vector Field and Field Lines
Two ways to describe the same thing
Dipole with +/-
Vector field Field lines
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15. More Vector Field and Field Lines
Dipole with +/+
Vector field Field lines
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16. Electric Field lines
Rank the electric field strength in order from largest to smallest. 1 3 2 4
A: E1 < E2 < E3 = E4
B: E3 = E4 < E2 < E1
C: E2 = E3 < E4 < E1
D: E1 < E4 < E2 = E3
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17. Electric Field of a “blob”
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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.
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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.
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20. Electric Field (continuous distribution)
(i)th bit of charge P
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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 DQ in 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.
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22. Problem
A thin rod of length L and charge Q. Find components of the electric field vector along the dotted line.
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23. Problem ans
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.
Determine the components of (Ex, Ey, …) at P due to chunk expressed in terms of variables (x, y, …r, q…).
Pick a generic chunk of charge DQ.
Identify, P, the place in space you want the field.
Draw a picture, pick a coordinate system. x y
ith P x
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24. Problem ans x
Add up contributions, sum becomes definite integral with limits corresponding to charge.
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25. Problem ans y
Add up contributions, sum becomes definite integral with limits corresponding to charge.
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26. Problem ans complete
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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
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28. Problem ans
(i)th bit of charge
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29. Field of quarter circle of charge
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30. Other charge geometries
Line
Hoop
Disk (from hoops)
Plane (from disk)
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31. Field of line (infinite)
Points directly away, decrease with distance
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32. Field of hoop, along axis
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33. Field of disk, along axis
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34. Field of plane (“infinite”)
perpendicular to the plane
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35. Plane from lots of lines (perpendicular to page)
Straighten up, no distance dependence
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36. Parallel-plate Capacitor
Net charge is zero
Charge lost from +Q side ends up on -Q side
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37. Find the electric field inside capacitor
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38. Phys 133

39. Rank the electric field strength at the 5 points for the ideal capacitor1 2 3 4 5
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40. Charges in an Electric Field
(due to charges; we can calculate)
Charge in Electric Field
(experiences a force)
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41. Problem 26.49
A plastic rod with charge Q = 1 mC and R = 0.1 m is bent into a quarter circle.
Using your past work, find the electric field at the origin.
Find the net force vector for a +1 mC charge located at the origin.
Find the net force for a -3 mC charge located at the origin.
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42. 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
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43. Dipole in an Electric Field
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44. Phys 133