What You Already Know

Transcription

1 What You Already Know Coulomb s law Electric fields Gauss law Electric fields for several configurations Point Line Plane (nonconducting) Sheet (conducting) Ring (along axis) Disk (along axis) Sphere Cylinder Dipole (along and axes) PHY2049: Chapter 24 1

2 Chapter 24: Electric Potential Electric Potential Energy Electric Potential Equipotential Surfaces Potential of Point Charge Potential of Charge Distribution Calculating the Field from the Potential Potential Energy from a System of Charges Potential of Isolated Charged Conductors PHY2049: Chapter 24 2

3 Reading Quiz: Chapter 24 An equipotential surface is: a) a surface where the electric field is constant b) always parallel to the electric field c) a surface where the potential is zero d) always perpendicular to the electric field e) a surface where the electric field is zero PHY2049: Chapter 24 3

4 The volt is a unit of: a) potential energy b) electric field c) potential d) force Reading Quiz: Chapter 24 PHY2049: Chapter 24 4

5 Electric potential is: Reading Quiz: Chapter 24 a) a scalar quantity b) a vector quantity c) can be either scalar or vector PHY2049: Chapter 24 5

6 Electric Work and Potential Energy From Physics 1 Find work moving object from A to B using constant force F W = F x x F is an example of a conservative force Work depends only on endpoints, not on path (e.g., 1, 2 or 3) Allows us to define potential energy More generally ( ) AB B A U U W = F x x ( ) B A AB B A U U F dx B A x x B A x x A B PHY2049: Chapter 24 6

7 Electric Work and Potential Energy Point charges Q, q: Work moving charge q from A B B BkQq WAB = F ds= rˆ ds rˆ ds= dr A A 2 r W AB Coulomb force is conservative (path independent) Potential energy of two point charges ( ) B = dr = A 2 r r = r r B kqq kqq kqq kqq kqq kqq kqq U ( ) B UA = WAB = U r = r r r B r r A A A B PHY2049: Chapter 24 7

8 Electric Force is Conservative Holds in all electrostatic situations (not just point charge) Proof: integrate over any charge distribution Work done by electric field moving charge q from i to f Calculate from difference of potential energies Charges i q f Work: Welec = Δ U fi = Ui U f PHY2049: Chapter 24 8

9 Problem: Electric Potential Energy Two identical +12 mc point charges are initially spaced 5 cm from each other. If they are released at the same instant from rest, how fast will they be moving when they are very far from each other? Assume m 1 = m 2 = 1.0 g. Ki + Ui = Kf + Uf 2 2 kq ( = 2 mv ) 0 2 f + v f = d i kq md i v f ( )( 0.012) ( 3 10 )( 0.05) = = m/s 2 5 PHY2049: Chapter 24 9

10 Gravitational & Electric Potential Energy Gravity A Electric h d B A B WG = mgh = UA U W B E = qed = UA UB Point B at lower potential energy than point A (q>0) PHY2049: Chapter 24 10

11 Electric Potential Potential = PE per unit charge Δ V =ΔU / q b Potential difference: constant E ( ) V V = E x x = Ed b a b a Potential difference: general E field b Vb Va = E ds a d E +Q Potential higher at + charges and falls to lower value at charges +q: Moves from higher to lower V q: Moves from lower to higher V a PHY2049: Chapter 24 11

12 Units of potential: volt Units for V and E V = U/q Volt = Joule / Coulomb Units of electric field F = Eq E = F/q Newton / Coulomb V = Ed E = V/d Volt / Meter PHY2049: Chapter 24 12

13 Example of Potential of Point Charge Point charge q (using V = 0 at r = ) V = kq r Example: Potential at surface of proton (r = m) V ( 9 )( ) kq 6 = = = = 1.44 MV r PHY2049: Chapter 24 13

14 Energy Units: Electron Volts 1 ev = energy of charge e accelerated through 1 Volt ( 19 ) 1eV = C i1v 19 = J Let q = 4e and V = 2000 V K K = = 8000eV = 8keV ( ) = = J PHY2049: Chapter 24 14

15 ConcepTest: Electric Energy A proton and an electron are each accelerated across a region of constant E field. Which has larger acceleration? (a) proton (b) electron (c) both have equal acceleration (d) neither one accelerates F = Ee a = F/m = Ee/m m e m p Electron is much lighter than proton PHY2049: Chapter 24 15

16 ConcepTest: Electric Energy Which has the biggest increase in KE? (a) proton (b) electron (c) both have the same increase in KE (d) KE = 0 for both K = Fd = Eed V e > V p PHY2049: Chapter 24 16

17 Equipotential Surfaces Equipotentials: Contours of constant potential No work to move charge along contour: W = -qδv = 0 E equipotential surface If E 0, would need work to move charge along surface See PHY2049: Chapter 24 17

18 Equipotential: Constant E Field Constant E Example: Capacitor PHY2049: Chapter 24 18

19 Equipotential: Point Charge Equipotentials PHY2049: Chapter 24 19

20 Equipotential: Dipole PHY2049: Chapter 24 20

21 Topographic Map: Equal Altitude Contours Contour: Line of constant gravitational potential PHY2049: Chapter 24 21