1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 7: June 3 rd 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Capacitors with Dielectrics Dielectric: nonconducting material (rubber, glass, mylar,…..) Simple experiment: 1)Charge a capacitor to charge Q and Voltage  V. 2)Disconnect capacitor from battery and connect it to a “Volt meter” (“Volt meters” measure electric potential differences) 3)Voltmeter shows a certain value  V o. 4)Insert a dielectric between capacitor plates.  Voltage between plates DECREASES to a new, lower value  V even though no charge was added to or removed from the capacitor. 5) Compare capacitances before and after insertion of dielectric:

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Dielectric Strength The maximum amount of charge that can be stored on a capacitor depends not only on the capacitance, but also on the “breakdown voltage” of the capacitor (capacitors will arc and sometimes self-destruct if the breakdown voltage is exceeded). Breakdown voltage depends on the dielectric strength of the material used. Dielectric strength is essentially the electric field strength at which the capacitor arcs. Thus it is measured in units of V/m.

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Electric Dipole Moment (vector p) - + 2a +q -q

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Torque on Electric Dipole in an Electric Field - + +q -q O

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 Potential Energy of Electric Dipole in an Electric Field

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Atomic Description of Dielectrics Polarized molecules: Average position of the positive charge is different from the average position of the negative charge. Polar molecules: permanently polarized Consider dielectric made from polar molecules (have a dipole moment) first: - + ++++++++ -------- Dipoles tend to align with electric field No field: randomly oriented dipoles

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Atomic Description of Dielectrics - + ++++++++ -------- Net positive surface charge induced Net negative surface charge induced

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Atomic Description of Dielectrics

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Conductor as “Dielectric”

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Example: Plate Capacitor Dielectric fills 1/3 of volume of capacitor as shown.  =2.3 A=4.0cm 2 d = 0.8cm Find ratio of capacitance with and without the dielectric.

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Example: Plate Capacitor – inserting uncharged conductor Conductor fills 1/3 of volume of capacitor as shown. A=4.0cm 2 d = 0.8cm Find ratio of capacitance with and without the conductor Surface charge equals “Q” and “-Q”

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 Example: Plate Capacitor Dielectric fills 1/3 of volume of capacitor as shown.  =2.3 A=4.0cm 2 d = 0.8cm Find ratio of capacitance with and without the dielectric.