Physics 1202: Lecture 2 Today’s Agenda Announcements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW assignments, solutions etc. Clicker: frequency code AA Homework #1: On Masterphysics this Friday Homeworks posted on Masteringphysics You need to register (included in cost of book) Go to First Day of Class on syllabus for details Course ID: cote90751 Problems: see Mairead Jacoby (Pearson) Chemistry Cafe Friday between 10:00AM – 2:00PM Labs start during the week of January 23. 1

Today’s Topic : Chap. 19 Review of Coulomb force Define Electric Field in terms of force on "test charge" Electric Field Lines Electric Field of a point charge Electric Field of plates Shielding and charging by induction Gauss’s law and applications

Recall Coulomb's Law Þ q2 r F12 q1 F21 q1q2 1 F12= r 4pe0 r2 1 4pe0 SI Units: r in meters q in Coulombs F in Newtons Þ 1 4pe0 = k = 8.987 109 N m2/C2 Charles Coulomb (1736-1806)

19-4 Electric Fields

Fields of all kinds... 77 73 72 75 82 71 77 84 68 80 64 73 83 82 88 55 66 88 80 75 88 90 83 92 91 These isolated Temperatures make up a Scalar Field (you learn only the temperature at a place you choose)

Fields of all kinds... It may be more interesting to know which way the wind is blowing … 77 73 72 75 82 71 77 84 68 80 64 73 83 57 56 55 66 88 80 75 88 90 83 92 91 That would require a VECTOR field. (you learn how fast the wind is blowing, AND in what direction)

Electric Fields The force, F, on any charge q0 due to some collection of charges is always proportional to q0: Introducing the Electric Field: a quantity, which is independent of that charge q0, and depends only upon its position relative to the collection of charges. A FIELD is something that can be defined anywhere in space it can be a scalar field (e.g., a Temperature Field) it can be a vector field (as we have for the Electric Field)

Lecture 2, ACT 1 (a) (b) (c) Both charges Q1 and Q2 must be positive. x y E d Two charges, Q1 and Q2 , fixed along the x-axis as shown, produce an electric field E at a point (x,y) = (0,d) which is directed along the negative y-axis. Which of the following statements is true? (a) Both charges Q1 and Q2 must be positive. (b) Both charges Q1 and Q2 must be negative. (c) The charges Q1 and Q2 must have opposite signs.

How Can We Visualize the E Field? + O Vector Maps: arrow length indicates vector magnitude Graphs: Ex, Ey, Ez as a function of (x, y, z) Er, Eq, EF as a function of (r, q, F) + chg x Ex

19-5: Another Way to Visualize E ... The Old Way: Vector Maps A New Way: Electric Field Lines Faraday 1791-1867 + chg - chg + O - + O Lines leave positive charges and return to negative charges Remember: test charge defining a field is positive Number of lines leaving/entering charge = amount of charge Tangent of line = direction of E Density of lines = magnitude of E

Electric field lines The charge on the right is twice the magnitude of the charge on the left (and opposite in sign), so there are twice as many field lines, and they point toward the charge rather than away from it. positive: 8 lines → +q negative: 16 lines → -2q

Various combinations of charges Note that, while the lines are less dense where the field is weaker, the field is not necessarily zero where there are no lines. In fact, there is only one point within the figures below where the field is zero—can you find it? dipole

Clicker question ! Two point charges, separated by 1.5 cm, have charge values of +2.0 and 4.0 C, respectively. Suppose we determine that 10 field lines radiate out from the +2.0- C charge. If so, what might be inferred about the 4.0-C charge with respect to field lines? a. 20 radiate out b. 5 radiate out c. 20 radiate in d. 10 radiate in

19.6 Conductor and shielding Excess charges in conductors: Free to move Repel each other End up on the surface At equilibrium No moving charges E = 0 inside (otherwise test charge would move …) Electric field perpendicular to surface Otherwise, a force would move charges Not at equilibrium !

19.6 Electric field near Conductors Conductor at equilibrium E perpendicular to surface E=0 inside General shape More charges at sharper curves E larger there Easier to accumulate charge in pointy objects Lightning rod

19.7 Electric Flux & Gauss’s Law Measures E ⏊ to surface A SI unit: N・m2 /C Flux of a point charge +q E = kq/r2 radially outward Choosing a sphere centered on q E is ⏊ to surface A

Gauss’s Law Defining permittivity of free space Gauss’s law electric flux through a closed surface is proportional to the charge enclosed by the surface:

Gauss’s Law Useful to get electric field Charged plate symmetry: E ⏊ to plate uniformly charged: s = q/A So E: constant magnitude Useful to get electric field By taking advantage of geometry

Electric Field Distibutions Summary Electric Field Distibutions Dipole ~ 1 / R3 Point Charge ~ 1 / R2 Infinite Line of Charge ~ 1 / R

Recap of today’s lecture Define Electric Field in terms of force on "test charge" Electric Field Lines Examples Charges in conductors Electric Flux and Gauss’s Law Homework #1 on Mastering Physics From Chapter 19