1. Electric Fields Review Coulomb’s Law Review Electric Fields
Multiple-charge Electric Fields
Continuous-charge Electric Fields
Parallel Plate Fields
Parallel Plate Examples
Gauss’s Law

2. Malaysian search
Estimate radius from satellite signal strength Heading?? (θ)???

3. Coulomb’s Law Fundamental property charge Positive and negative charge
Units Coulombs (C)
Force Law

4. Compare with gravitation
Fundamental property mass
Positive mass only
Units kilograms (kg)
Force Law

5. “Field” concept - Gravity
Newton’s Universal Law of Gravitation
𝐹= 𝐺 𝑚 1 𝑚 2 𝑟 2
One-step process (tedious)
𝐹 𝑥 = 𝐺𝑀 𝑚 𝑥 𝑟 2
𝐺𝑀 𝑚 𝑐𝑎𝑟 𝑟 𝐺𝑀 𝑚 𝑡𝑟𝑢𝑐𝑘 𝑟 𝐺𝑀 𝑚 𝑝𝑒𝑑 𝑟 2
Two-step process (simple)
𝑔= 𝐺𝑀 𝑟 2 =9.8 𝑁/𝑘𝑔
𝐹 𝑥 = 𝑚 𝑥 𝑔
𝑚 𝑐𝑎𝑟 𝑔 𝑚 𝑡𝑟𝑢𝑐𝑘 𝑔 𝑚 𝑝𝑒𝑑 𝑔

6. “Field” concept - Electrical
Cellphone signal
Multiple users sharing same tower.
Why calculate each phone separately?
2 step process
1. Calculate common “field”.
2. Calculate each phone’s interaction with that “field”.
“Field” equals # of “bars” you have!

7. Electrostatic vs. Gravitational Field
In gravitation we calculate
𝐹= 𝐺𝑀 𝑟 2 𝑚
Bracket part becomes “g”
In electrostatic we calculate
𝐹= 𝑘𝑄 𝑟 2 𝑞
Bracket part becomes “E”

8. Electric Field Animation

9. Electric Field - Example 16-9 (1)
Get magnitudes
𝐸 2 =𝑘 𝑞 2 𝑟 = 9∙ 𝑁 𝑚 2 𝐶 ∙ 10 −6 𝐶 𝑚 2 =5∙ 𝑁/𝐶
𝐸 1 =𝑘 𝑞 2 𝑟 = 9∙ 𝑁 𝑚 2 𝐶 ∙ 10 −6 𝐶 𝑚 2 =1.25 ∙ 𝑁/𝐶

10. Electric Field - Example 16-9 (2)
XY table
Field
X-component
Y-component E2
0 N/C
+5 x 106 N/C E1
+1.1 x 106 N/C
x 106 N/C
Total
x 106 N/C

11. Electric Field – Problem 16
Charge square

12. Continuous charge distributions
Coulomb’s Law plus a lot of integral calculus!
(don’t worry, I’ll just show results)
Field of line of charge
Field of ring of charge
Field of sheet of charge
Field between 2 sheets of charge

13. 1- Field of Line of Charge

14. 2 – Field of Ring of Charge

15. 3 – Field of Sheet of Charge

16. Continuous charge distributions - Summary

17. 4 – Field between 2 Sheets of Charge
In region between parallel plates
𝐸= 𝑄 𝜀 𝑜 𝐴 = 𝜎 𝜀 𝑜
𝑄=𝑐ℎ𝑎𝑟𝑔𝑒 𝑜𝑛 𝑒𝑎𝑐ℎ 𝑝𝑙𝑎𝑡𝑒
𝜎=𝑐ℎ𝑎𝑟𝑔𝑒 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑛 𝑒𝑎𝑐ℎ 𝑝𝑙𝑎𝑡𝑒
𝐴=𝐴𝑟𝑒𝑎 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑝𝑙𝑎𝑡𝑒
𝜀 𝑜 = 1 4𝜋𝑘 = 8.85∙ 10 −12 𝐶 2 𝑁 𝑚 2
Note: now the field is constant
Coulomb’s Law Lots of integral calculus = Constant fields
𝐸= 𝑘𝑄 𝑟 𝑑𝑥 𝜎 𝜀 𝑜
(and we just show results)

18. Field between 2 Sheets of Charge
In region between parallel plates
𝐸= 𝑄 𝜀 𝑜 𝐴 = 𝜎 𝜀 𝑜
Note field is constant between plates
Uses for parallel plates
Capacitors (charge storage)
Beam accelerators / deflectors (old TVs, high-energy labs)
Semiconductor junctions
Photocopy machines

19. Example - Photocopy Field
Electrostatic for twice weight
𝑞𝐸−2𝑚𝑔=0
𝐸= 2𝑚𝑔 𝑞
= 2 9∙ 10 −16 𝑘𝑔 𝑚 𝑠 ∙ 10 −19 𝐶 =5500 𝑁/𝐶

20. Examples Problem 23 Problem 24
𝐹=𝑞𝐸= −1.6∙ 10 −19 𝐶 𝑁 𝐶 =−4.16∙ 10 −16 𝑁 𝑤𝑒𝑠𝑡
Problem 24
𝐸= 𝐹 𝑞 = 3.75∙ 10 −14 𝑁 1.6∙ 10 −19 𝐶 =234,000 𝑁 𝐶 𝑠𝑜𝑢𝑡ℎ

21. Examples 𝐹=𝑚𝑎 Problem 27 Problem 31
𝐹=𝑞𝐸= −1.6∙ 10 −19 𝐶 𝑁 𝐶 =−1.2∙ 10 −16 𝑁
𝑎= 𝐹 𝑚 = −1.2∙ 10 −16 𝑁 9.1∙ 10 −31 𝑘𝑔 =1.32∙ 𝑚 𝑠 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛
Problem 31
𝐹=𝑚𝑎
𝐸= 𝐹 𝑞

22. Field Lines
Field lines start at (+) charge, end at (-) charge. Without charge, field lines don’t exist.
A (+) test charge moves in the direction of the field lines, a (-) test charge moves opposite the direction of field lines.
The cross-sectional density of field lines is proportional to the electric field strength. 𝐸∝ 𝐿𝑖𝑛𝑒𝑠 𝐴𝑟𝑒𝑎

23. Gauss’s Law
Number of field lines entering or leaving any volume proportional to charge enclosed.
𝐸∙𝑑𝐴 𝑐𝑜𝑠𝜃= 𝑞 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝜀 𝑜
Evaluate over entire closed surface
Field lines perpendicular to surface
Need to know symmetry

24. Gauss’s Law Examples
Point charge
Line of charge
Sheet of charge

25. Gauss’s Law 1 – Point charge
𝐸∙𝑑𝐴 𝑐𝑜𝑠𝜃= 𝑞 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝜀 𝑜
For spherical surface
𝐸 4𝜋 𝑟 2 = 𝑞 𝜀 𝑜
𝐸 = 𝑞 4𝜋 𝑟 2 𝜀 𝑜

26. Gauss’s Law 2 – Line charge
𝐸∙𝑑𝐴 𝑐𝑜𝑠𝜃= 𝑞 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝜀 𝑜
For cylindrical surface
𝐸 2𝜋𝑟𝑙= 𝜆𝑙 𝜀 𝑜
𝐸 = 𝜆 2𝜋𝑟𝜀 𝑜

27. Gauss’s Law 3 – Sheet charge
𝐸∙𝑑𝐴 𝑐𝑜𝑠𝜃= 𝑞 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝜀 𝑜
For pillbox surface
𝐸 2𝐴= 𝜎𝐴 𝜀 𝑜
𝐸 = 𝜎 2𝜀 𝑜