Force and Work: Reminder

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Drusilla Pope
5 years ago
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1 Electic Potential

2 Foce and Wok: Reminde Displacement d a: initial point b: final point Reminde fom Mechanics: Foce F if thee is a foce acting on an object (e.g. electic foce), this foce may do some wok when the object moves Electic Potential 2

3 Foce and Wok W a b Fd cos that s why diection mattes d a: initial point F b: final point F F F Wok can be positive (ϕ<90º) o negative (ϕ>90º) Electic Potential 3

4 Consevative Foce If a foce is consevative, thee is something called potential enegy U which changes fom point to point b: final point U a a: initial point U b W ab Wok does not depend on the path! U Electic Potential 4 a U b

5 Wok-Enegy Theoem Change in kinetic enegy = wok K K b b K K a a W U ab a U b total enegy doesn t change K a U a K b U b Electic Potential 5

6 Electic Potential Enegy If chage q is placed in electic field E, the foce acting on it is F qe U a U b W ab qed cos q E v v 1 2 Electic Potential 6

7 Electic Potential Foce Field = Foce divided by pobe chage q Field is independent of q Potential enegy Potential = Potential enegy divided by pobe chage q Potential is independent of q U q [] = olt 1 = 1 J / C Electic Potential 7

8 watch signs! Electic Potential Diffeence Like potential enegy, potential itself is meaningless, what makes sense is the potential diffeence ba W ab q q E potential diffeence ( voltage ) between points a and b ba b a chage acceleates a: high potential b: low potential Electic Potential 8

9 Relation between Electic Potential Diffeence and Electic Field W a ba qed cos b W ab q Ed ba conside a pobe chage moving paallel to electic field lines d E a: high potential b: low potential Electic Potential 9

10 Field of Point Chage Chage poduces electic field which can act on anothe chage thee is potential enegy due to inteaction of two chages y q Field is non-unifom Field is not constant x E k 2 Electic Potential 10

11 Wok in Field of Point Chage y E k 2 ϕ=0, OK q W qed cos a b x E vaies with x, not OK! Need calculus to compute esult Electic Potential 11

12 Wok in Field of Point Chage W a b kq 1 a 1 b k q a k q b q U k Fomula valid fo any combination of q, q signs Electic Potential 12

13 Moe about potential enegy U is always defined w..t. U at some point chosen by convention (only U a -U b has physical meaning) ou choice: U=0 at = What if thee ae moe than one chage? q U kq Electic Potential 13

14 Potential of a Point Chage U q k Fo many point chages: k Both potential and electic field ae independent fom test chage Potential is a scala, field is a vecto Electic Potential 14

15 Equipotential Sufaces electic field lines equipotential sufaces electic field line: imaginay line which in each point is tangent to electic field vecto E equipotential suface: potential is the same at evey point two equipotential sufaces neve touch o intesect equipotential sufaces ae mutually pependicula to field lines Electic Potential 15

16 Unifom Field y U Ey q E const y const x equipotential sufaces = planes pependicula to y axis Electic Potential 16

17 Point Chage k const const equipotential sufaces = sphees with centes at oigin Electic Potential 17

18 Dipole If chages +q and q ae placed at y=+a and y= a then plane y=0 is an equipotential suface Poof: k 1 2 at y=0 1 = 2, so =0 Electic Potential 18

19 Potential Gadient The magnitude of the electic field at any point on an equipotential suface = ate of change of potential Electic Potential 19 s E as a point moves along electic field, potential deceases electic field is a vecto, so what about diection? z y x E z y x s,, ),, (

conducto 2 has chage q 2, but we ll always assume q 1 == q 2, so the net chage is 0

20 Capacito and capacitance Capacito = device which stoes electic chage Capacito battey! Capacito = two conductos sepaated by an insulato geneally, conducto 1 has chage q 1, and conducto 2 has chage q 2, but we ll always assume q 1 == q 2, so the net chage is 0 Capacitance C = capacito s ability to stoe chage C [C] = Faad, 1 F = 1 C / Electic Potential 20

21 Paallel-Plate Capacito E C A 0 Ed suface chage density this can be poved using Gauss law C 0 d ε 0 =1/4πk= C 2 /N m 2 A E Electic Potential 21

22 Dielectics If thee is some mateial between the capacito plates, the capacitance inceases due to polaization K E C C 0 K E K 0 0 K = dielectic constant (a pue numbe depending on mateial) If we inset mateial inside capacito chaged with chage, the voltage deceases by K Electic Potential 22

23 Electic Field Enegy Potential enegy of a capacito = wok needed to chage it If thee is aleady chage and we want to add moe chage then we need to do wok W= W C U W total 2 2 2C C 2 2 W total Electic Potential 23

24 Electic Field Enegy Density Enegy density u = enegy U pe unit volume v v Ad U u v 0 A C d Ed 2 C 2Ad u 0E 2 thee is nothing elated to a capacito in this fomula it s also valid fo a field in vacuum! 2 Electic Potential 24

17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other

17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system