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 Point charges q 1, q 2 : Work moving charge q 2 from A B B Bkq1q 2 WAB = F ds = rˆ ds rˆ ds = dr A A 2 r B kq q kq q kq q WAB = = A r 1 2dr ra rb Path independence: conservative force Define potential energy of two point charge U U W U = B A AB kq q ( ) 1 2 r Depends only on endpoints Path independent Like gravitation PHY2049: Chapter 24 6

7 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 7

8 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 8

9 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 9

10 Electric Potential Potential = PE per unit charge V = U/ q b Potential difference: general E field b Vb Va = E ds a Potential difference: constant E d E +Q V V = Ed a b 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 10

11 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 11

12 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 12

13 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 13

14 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 14

15 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 15

16 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 16

17 Equipotential: Constant E Field Constant E Example: Capacitor PHY2049: Chapter 24 17

18 Equipotential: Point Charge Equipotentials PHY2049: Chapter 24 18

19 Equipotential: Dipole PHY2049: Chapter 24 19

20 Topographic Map: Equal Altitude Contours Contour: Line of constant gravitational potential PHY2049: Chapter 24 20

21 Calculating E From Electric Potential V Electric field in terms of potential du = F ds = Fxdx Fydy Fz dz dv = E ds = E dx E dy E dz x y z V V V Ex = Ey = Ez = x y z Divide by q PHY2049: Chapter 24 21

22 Example: Electric Field of Point Charge Get E by differentiating potential ( 2 2 2) 1/2 r = x + y + z V = kq r E x kq kqx kqx = = = x 1/2 3/2 3 r ( 2 2 2) ( x + y + z x + y + z ) E y, E etc. z E kq x y z kq = r r r r r 2,, r 2 ˆ Coulomb s law PHY2049: Chapter 24 22