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

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

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

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

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

7 Potential Difference & Average Electric Field Let + test charge q move in the direction of the field E (  °)  U E = -W E  U E = -F E d  U E = -qE av d

8 Ex. Average Electric Field X(m)V(volts) Interval 0 to 2 2 to to to 50

9 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 The capacitance is defined as C = Q/V Units: C/V = farad = F Units: C/V = farad = F

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

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

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

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

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

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

18 Capacitors in “Parallel” Arrangement Ex.

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

20 Summary W electric = qEd = -  EPE V =  EPE/q V = V1 + V2 +… E avg = -ΔV/d C = q/V = K  o A/d Capacitor Energy = ½CV 2 Capcitors in series & parallel