Fun with Capacitors - Part II

1. Fun with Capacitors - Part II

2. This week • Wednesday • Yell at you about the exam. • Capacitors II • Friday • Finish Caps • Start Current and Resistance • Monday • Quiz – Caps & Current (Through Friday’s stuff)

3. Capacitor Circuits

4. A Thunker If a drop of liquid has capacitance 1.00 pF, what is its radius?

5. Anudder Thunker Find the equivalent capacitance between points a and b in the combination of capacitors shown in the figure. V(ab) same across each

6. E=e0A/d +dq +q -q More on the Big C • We move a charge dq from the (-) plate to the (+) one. • The (-) plate becomes more (-) • The (+) plate becomes more (+). • dW=Fd=dq x E x d

7. So…. Sorta like (1/2)mv2

8. Parallel Plate Cylindrical Spherical Not All Capacitors are Created Equal

9. Spherical Capacitor

10. Calculate Potential Difference V (-) sign because E and ds are in OPPOSITE directions.

11. Continuing… Lost (-) sign due to switch of limits.

12. What's Happening? DIELECTRIC

13. Polar Materials (Water)

14. Apply an Electric Field Some LOCAL ordering Large Scale Ordering

15. Adding things up.. - + Net effect REDUCES the field

16. Non-Polar Material

17. Non-Polar Material Effective Charge is REDUCED

18. We can measure the C of a capacitor (later) C0 = Vacuum or air Value C = With dielectric in place C=kC0 (we show this later)

19. How to Check This Charge to V0 and then disconnect from The battery. C0 V0 Connect the two together V C0 will lose some charge to the capacitor with the dielectric. We can measure V with a voltmeter (later).

20. V Checking the idea.. Note: When two Capacitors are the same (No dielectric), then V=V0/2.

22. Messing with Capacitors The battery means that the potential difference across the capacitor remains constant. For this case, we insert the dielectric but hold the voltage constant, q=CV since C  kC0 qk kC0V THE EXTRA CHARGE COMES FROM THE BATTERY! + V - + - + - + V - Remember – We hold V constant with the battery.

23. Another Case • We charge the capacitor to a voltage V0. • We disconnect the battery. • We slip a dielectric in between the two plates. • We look at the voltage across the capacitor to see what happens.

24. No Battery q0 + - + - q0 =C0Vo When the dielectric is inserted, no charge is added so the charge must be the same. V0 V qk

25. Another Way to Think About This • There is an original charge q on the capacitor. • If you slide the dielectric into the capacitor, you are adding no additional STORED charge. Just moving some charge around in the dielectric material. • If you short the capacitors with your fingers, only the original charge on the capacitor can burn your fingers to a crisp! • The charge in q=CV must therefore be the free charge on the metal plates of the capacitor.

26. ++++++++++++ q V0 ------------------ -q A Closer Look at this stuff.. Consider this virgin capacitor. No dielectric experience. Applied Voltage via a battery. C0

27. ++++++++++++ q V0 ------------------ -q Remove the Battery The Voltage across the capacitor remains V0 q remains the same as well. The capacitor is fat (charged), dumb and happy.

28. ++++++++++++ q - - - - - - - - -q’ +q’ V0 + + + + + + ------------------ -q Slip in a DielectricAlmost, but not quite, filling the space Gaussian Surface E E’ from induced charges E0

29. A little sheet from the past.. -q’ +q’ - - - +++ -q q 0 2xEsheet 0

30. Some more sheet…

31. A Few slides backNo Battery q=C0Vo When the dielectric is inserted, no charge is added so the charge must be the same. q0 + - + - V0 V qk

32. From this last equation

33. + - Vo Another look

34. Original Structure Disconnect Battery Slip in Dielectric Vo + - + - + - Add Dielectric to Capacitor V0 Note: Charge on plate does not change!

35. so so si + si - + - What happens? Potential Difference is REDUCED by insertion of dielectric. Charge on plate is Unchanged! Capacitance increases by a factor of k as we showed previously

36. SUMMARY OF RESULTS

37. APPLICATION OF GAUSS’ LAW

38. New Gauss for Dielectrics