Electric forces, fields & potential

1. Electric forces, fields & potential Prof. Nikola Tesla (seated) 授課：楊順聰教授，朱唯勤教授 國立陽明大學醫學工程研究所

2. Relation among force, field, potential • Coulomb’s Law: F = (kqQ/r2)r • K = 9.0*109 Nm2/C2; q = 1.6*10-19 C • Vector and follows superposition principle •  r-2 (like gravitational force) • Following classical physics, but with positive & negative

3. Electric field, E • Electric Field: E = (kQ/r2)r • A physical quantity created by charge(s) • F = qE • Range where force reaching • Vector summation • E = E1 + E2 + … = (F1 + F2 + … ) / q

4. Charge & force

5. Shark

6. Fish to detect object

7. Electric field effects

8. Electric field & line

9. Electric line

10. Electric field • Combination field Ei = (kQi / r2)r, i = 1, 2, … • E = E1 + E2 + …

11. Electric dipole a

12. Electric dipole – con’d

13. Electric field on surface • Skin effect • Charge static on surface

14. Fields due to continuous distributions of charge Continuous charge distributions

15. Charge density • Surface charge density • Volume charge density

16. Electric charge • Condense charge E = (kQ/r2)r

17. Properties of Electric fields • Concentric spherical shells: • E =4pks?

18. Electric field of parallel planes • Analogy to the concentric spherical shells when looking into a very small scale … • E = 4pks • Q: s = ?

19. E field of a single charged plate • Charged infinite plane: E = 2pks (s: Q/A) • Analogy to a finite charged plane???

20. E field of a charged conducting plate • Outside: E = 4pks • Q: E = 2 x E thin plane? • Q: s = ? • Inside: E = 0 • E is perpendicular • Only surface charges

21. Properties of electric fields • What mostly are true for a conducting plate also hold for any shape of conductors • E = 4pks outside • E = 0 inside • E is perpendicular (just outside the surface)

22. Electric field within conductor

23. Electric Potential, V • Electric Potential: • Work to move a charge within field • V = Y / q = (kQ/r) • 1 Volt = 1 J / C • Electric potential energy, Y, per unit charge • Y= qE•Dr= (kqQ/r) • V = E•Dr = E Dr cosq • Scale independent on method, time …

24. Cloud & Storms

25. Electric field & potential • Electric potential energy:Y = qE•Dr =(kqQ/r) • Electric potential: V = Y / q = (kQ/r) • Vab= Ed, where d is the distance along E

26. Electric potential for a point charge

27. Electric potential for a dipole q p a a r

28. Electric potential for a uniform E • For oppositely charged plates • E = 4pks = 4pkQ/A • V = 4pkQd/A

29. Capacitor, capacitance • Capacitor: Two conductors separated by an insulator (or vacuum) • Capacitance: a measure of the charge maintained at a given potential • Examples: ions among cell membranes, electrical circuits, TV, computer, etc.

30. Capacitor • E = 4pks = 4pkQ/A • V = 4pkQd/A • C = Q/V = A/(4pkd) =(e0A/d) • e0 = 8.85*10-12 F/m

31. Charging a capacitor

32. Energy stored in a capacitor v V V = q / C Vi = qi / C q Q qi

33. Potential energy within capacitor • UE=QV/2 =(Q2/C)/2 =CV2/2 • =(e0A/d)(Ed)2/2 • =e0(Ad)E2/2 • Energy density=e0E2/2

34. Combination of capacitors

35. Dielectric • Dielectric constant k = C/C0 • C = e0kA/d = eA/d • =(1/2) e0AdE2 • Energy density = (1/2) e0kE2

36. Dielectric strength Dielectric Strength (V/m) 3×106 1×107 2×108 2×107

37. Capacitance application • Battery • Tuner • Sensor • Change area • Change distance • Change dielectric property

38. Oscilloscope

39. The oscilloscope Q: How to control where on the CRT screen the electron would hit? x D d l E

40. Immunologically sensitive field-effect sensor