Physics 1202: Lecture 2 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, solutions etc. Homework #1:Homework #1: –On Masterphysics this Friday Homeworks posted on Masteringphysics –You need to register (included in cost of book) –Go to masteringphysics.com and register Course ID: MPCOTE62465 Labs: Begin in two weeks (Sept. 14)

Today’s Topic : Continuing Chapter 15 –Review of Coulomb force –Examine the strength of electric forces –Define Electric Field in terms of force on "test charge" –Electric Field Lines –Electric Field of a point charge –Electric Field of an electric dipole Demonstration of Mastering Physics

Coulomb's Law SI Units: r in meters q in Coulombs F in Newtons  F 12 = 1 4   q1q2q1q2 r2r2 1 = N m 2 /C 2 r q2q2 r F 12 q1q1 F 21 r Charles Coulomb ( )

Force Comparison Electrical vs Gravitational  For a proton, q = 1.6 X C m = 1.67 X kg  * Note: smallest charge seen in nature ! q2q2 r q1q1 G= N m 2 /kg 2

How Strong is the Electrical Force? Really? Richard Feynman, The Feynman Lectures: "If you were standing at arm's length from someone and each of you had one percent more electrons than protons, the repelling force would be incredible. How great? Enough to lift the Empire State Building? No! To lift Mount Everest? No! The repulsion would be enough to lift a "weight" equal to that of the entire earth! " Richard Feynman ( ) Nobel Prize for QED Educator Extraordinaire For more info, check: The Character of Physical Law Surely You're Joking, Mr. Feynman What Do You Care What Other People Think?

Should we believe this? How many electrons in a person? What do we assume is the chemical composition of a person? Simplify: assume water (molecular weight = 18) What then is the number of electrons/gram in a person? So, how many electrons in a person? How much charge is 1% of electrons in a person? 6  molecules/mole 18 g/mole  10 e  /molecule = 3.3  e  /g 3.3  e  /g  80 kg = 2.6  e  1%  2.6  e   1.6  C/e  = 4.2  10 7 C Assume mass = 80 kg

Should we believe this? What is the force between 2 people an arm's length apart if they each had an excess of 1% electrons? What is the weight of the earth? Yes, that's INCREDIBLE!! F = ( 9  10 9 N-m  /C 2 )   4.2  10 7 C 0.75 m  F = 2.8  N W earth = 6  kg  m/s  W earth = 5.9  N

Fields of all kinds These isolated Temperatures make up a Scalar Field (you learn only the temperature at a place you choose)

Fields of all kinds That would require a VECTOR field. (you learn how fast the wind is blowing, AND in what direction) It may be more interesting to know which way the wind is blowing …

Electric Fields Introducing the Electric Field: a quantity, which is independent of that charge q, and depends only upon its position relative to the collection of charges. The force, F, on any charge q due to some collection of charges is always proportional to q: 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)

Example What is the electric field at the origin for this collection of charges? +q a a a a a x y If a charge Q were placed at the origin, the force on this charge would be: – The fields from the top right and bottom left cancel at the origin!! – The total field is then just the field from the top left charge, which points away from the top left charge as shown. – The components of the field are then: Note: if Q>0, F= if Q<0, F=

Lecture 2, ACT 1 Two charges, Q 1 and Q 2, 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 Q 1 and Q 2 must be positive. Q2Q2 Q1Q1 x y E d (b) Both charges Q 1 and Q 2 must be negative. (c) The charges Q 1 and Q 2 must have opposite signs.

How Can We Visualize the E Field? Vector Maps: arrow length indicates vector magnitude + chg + O Graphs: E x, E y, E z as a function of (x, y, z) E r, E , E  as a function of (r, ,  ) x ExEx

Example Consider a point charge fixed at the origin of a co-ordinate system as shown. –The following graphs represent the functional dependence of the Electric Field. Q x y r  r 0 ErEr  0 22 ErEr As the distance from the charge increases, the field falls off as 1/r 2. At fixed r, the radial component of the field is a constant, independent of  !! E

Lecture 2, ACT 2 x Consider a point charge fixed at the origin of a co-ordinate system as shown. –Which of the following graphs best represents the functional dependence of the Electric Field at the point (r,  )? Q y r  Fixed r>0  0 22 ExEx  0 22 ExEx  0 22 ExEx

Another Way to Visualize E... The Old Way: Vector Maps Lines leave positive charges and return to negative charges Number of lines leaving/entering charge = amount of charge Tangent of line = direction of E Density of lines = magnitude of E + O A New Way: Electric Field Lines + chg - chg + O  O

Homework #1 on Mastering Physics –From Chapter 15 Recap of today’s lecture Define Electric Field in terms of force on "test charge" Electric Field Lines Examples