1. 0 16 Overview • work, energy, voltage • relation between field and voltage • capacitance • homework: • 4, 8, 9, 13, 19, 40, 41, 55, 69, 82, 95, 97

2. 0 Electrostatic Potential Energy, UE& Electric Potential, V • Charge-charge interaction stores energy • Ex. two + + close have high UE • Electric Potential V is energy per test chargein (J/C = V) (volts) • Two steps to find V at a point of interest “P”: • 1) Measure DUE when q is moved to P (from far away) • 2) Calculate V = DUE/q • /

3. Work-Energy Theorem • Relates change in energy stored in a system to work done by that system. • DUE = -WE • If positive work is done by an electric system, then the change in the stored energy is negative.

4. Example V calculation • q = +1.0 C moved close to another + charge (from far away). • If DUE = +3.0 J, • Then V = DUE/q = (+3.0 J)/(+1.0 C)

5. Point Charge Potential, VQ • VQ = kQ/r • Ex. Potential 2.0m from Q = +4.0nC is VQ = kQ/r = (9E9)(+4E-9)/(2) = +18V. • Electric Potential is + near +charges • Ex. Potential 4.0m from Q = -4.0nC is VQ = kQ/r = (9E9)(-4E-9)/(4) = -9V. • Electric Potential is - near -charges • /

6. Potential Due to Several Charges • Point charge potentials add algebraically • VP = VQ1 + VQ2 + … • Ex. If “P” is 2.0m from Q1 = +4nC and 4.0m from Q2 = -4nC, Then

7. 0 Potential Difference & Average Electric Field • Let + test charge q move in the direction of the field E (q = 0°) • DUE = -WE • DUE = -FEd • DUE = -qEavd

8. 0 Ex. Average Electric Field

9. 0 Equipotential Surfaces • surfaces which have the same potential at all points. • Ex. A sphere surrounding an isolated point charge is an equipotential surface. • Ex. A charged conductor in electrostatic equilibrium is an equipotential surface. (this also implies E near surface is perpendicular to the surface)

10. Capacitance: Charge Stored per Volt Applied 0 The capacitance is defined as C = Q/V Units: C/V = farad = F

11. Capacitors • store energy… and give it back fast, e.g. flash unit

12. Permittivity • Relates to ability of material to store electrostatic potential energy • Empty space value: • Material values are: • … k is the dielectric constant • Exs. k = 1.0 air, 3.5 paper

13. Parallel Plate Capacitance • Ex. Area A = 100 square-cm, d =1mm

14. Energy Stored in a Capacitor Charge Q added to Capacitor over average potential of V/2

15. Capacitor Energy

16. Supercapacitors • Porous structure with high internal surface area (A) and small spacing (d) resulting in very large capacitance • Have capacitances greater than 1 farad

17. Capacitor Circuits • Parallel: each gets potential V, so capacitance increases • Series: each gets potential less than V, so capacitance decreases

18. Capacitors in “Parallel” Arrangement 0 Ex.

19. Capacitors in “Series” Arrangement 0 Q = 0 Ex.

20. Summary • Welectric = qEd = -DEPE • V = DEPE/q • V = V1 + V2 +… • Eavg = -ΔV/d • C = q/V = KeoA/d • Capacitor Energy = ½CV2 • Capcitors in series & parallel