1. Capacitor Circuits

2. Thunk some more … C 1 C 2 V C3C3 C1=12.0  f C2= 5.3  f C3= 4.5  d (12+5.3)pf

3. So…. Sorta like (1/2)mv 2

4. DIELECTRIC

5. Polar Materials (Water)

6. Apply an Electric Field Some LOCAL ordering Larger Scale Ordering

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

8. Non-Polar Material

9. Effective Charge is REDUCED

10. We can measure the C of a capacitor (later) C 0 = Vacuum or air Value C = With dielectric in place C=  C 0 (we show this later)

11. How to Check This Charge to V 0 and then disconnect from The battery. C0C0 V0V0 Connect the two together V C 0 will lose some charge to the capacitor with the dielectric. We can measure V with a voltmeter (later).

12. Checking the idea.. V Note: When two Capacitors are the same (No dielectric), then V=V 0 /2.

14. Messing with Capacitors + V - + V - +-+-+-+- 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   C 0 q    C 0 V THE EXTRA CHARGE COMES FROM THE BATTERY! Remember – We hold V constant with the battery.

15. Another Case  We charge the capacitor to a voltage V 0.  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.

16. No Battery +-+-+-+- q0q0 qq q 0 =C 0 V o When the dielectric is inserted, no charge is added so the charge must be the same. V0VV0V

17. A Closer Look at this stuff.. Consider this capacitor. No dielectric experience. Applied Voltage via a battery. C0C0 ++++++++++++ ------------------ V0V0 q -q

18. Remove the Battery ++++++++++++ ------------------ V0V0 q -q The Voltage across the capacitor remains V 0 q remains the same as well. The capacitor is (charged),

19. Slip in a Dielectric Almost, but not quite, filling the space ++++++++++++ ------------------ V0V0 q -q - - - - + + + -q’ +q’ E0E0 E E’ from induced charges Gaussian Surface

20. A little sheet from the past.. ++++++ ------ q -q -q’ +q’ 0 2xE sheet 0

21. Some more sheet…

22. A Few slides back No Battery +-+-+-+- q0q0 qq q=C 0 V o When the dielectric is inserted, no charge is added so the charge must be the same. V0VV0V

23. From this last equation

24. Add Dielectric to Capacitor Original Structure Disconnect Battery Slip in Dielectric +-+- VoVo +-+- +-+- V0V0 Note: Charge on plate does not change!

25. SUMMARY OF RESULTS

26. APPLICATION OF GAUSS’ LAW

27. New Gauss for Dielectrics