Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric charge Forces between charged objects The field model and the electric field Forces and torques on charged objects in electric fields Chapter 20 Electric Forces and Fields Topics: Sample question: In electrophoresis, what force causes DNA fragments to migrate through the gel? How can an investigator adjust the migration rate? Slide 20-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What to do to do well in this class A.Focus on key physics concepts May seem like basics but will help you solve even complex problems Focus on principle rather than recipes Need to have a functional understanding of key concepts Express key equations as sentences Know where they come from and what they mean Know how and when to apply them Know which equations are general and which are special cases Must know when not to apply special cases Look at a problem after a good physics diagram and maybe a good physical diagram and know what key physics concepts apply in that problem Memorize key concepts so you can look at a problem, say that’s Newton 2, and know the associated equation in a snap Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

What to do to do well in this class A.Focus on key physics concepts How to do this When you look at problems, mentally group problems by the physics rather than the physical situation After each class or at least each week, create a notesheet to organize a structure of the new key concepts for each chapter and note how they fit in with previous key concepts Use the note sheet to do homework problems (a) do as many homework problems as you can just using this sheet. (b) then go to your notes and the textbook for your missing pieces Use flash cards to memorize key concepts - include the concept description, relevant equations, diagrams, and what types of problems benefit from using that concept Pay close attention to examples done in class and note the physics and assume/observes in each example and how these are used Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

Coulomb Force Problems 1.Sum of Electric Forces from Point Charges 2.Levitation 3.Static Equilibrium 4.Comparing Electric Forces and Gravitational Forces

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Force of Gravity Slide 6-35

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Two 0.10 g honeybees each acquire a charge of +23 pC as they fly back to their hive. As they approach the hive entrance, they are 1.0 cm apart. What is the magnitude of the repulsive force between the two bees? How does this force compare with their weight? Example Problem 1 Slide 20-33

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A typical bowling ball is spherical, weighs 16 pounds, and has a diameter of 8.5 in. Suppose two bowling balls are right next to each other in the rack. What is the gravitational force between the two—magnitude and direction? What is the magnitude and direction of the force of gravity exerted by the Earth on one of the bowling balls? What is the magnitude and direction of the force of gravity on a 60 kg person? Example Problem 2 Slide 6-36

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Coulomb’s Law and Three Charges Two charged particles, with charges q 1 = +q and q 2 = +4q, are located at a distance d = 2 cm apart on the x axis. Where can a 3 rd charge be placed so that this 3 rd charge has F e net = 0 N, i.e the 3 rd charge is in equilibrium. Hint: Draw a diagram of the electric forces on the 3 rd charge in various positions. What are the conditions of equilibrium?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Coulomb’s Law and Three Charges Two charged particles, with charges q 1 = +q and q 2 = +4q, are located at a distance d = 2 cm apart on the x axis. Where should a third charged particle, with charge q 3 = +q, is placed so that F e net = 0 (equilibrium). For equilibrium, there are 3 conditions Charges must be on x-axis F e,1=>3 = F e,2=>3 The two forces must point in opposite directions

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Three charges in a line (change the problem) Two charged particles, with charges q 1 = -q and q 2 = +4q, are located at a distance d = 2 cm apart on the x axis. Where should a third charged particle, with charge q 3 = +q, is placed so that F e net = 0 (equilibrium). For equilibrium, there are 3 conditions Charges must be on x-axis F e,1=>3 = F e,2=>3 The two forces must point in opposite directions

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Introduction to Electric Field 1.Find the Electric force from a 9.00e-6 C charge on the following charges at 1m, 2m, and 3 m. a) 3.00e-6 C b) -4.00e-6 C c) -10.0e-6 C

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Introduction to Electric Field 1.Find the Electric force from a 9.00e-6 C charge on the following charges at 1m, 2m, and 3 m. a) 3.00e-6 C b) -4.00e-6 C c) -10.0e-6 C 2.Find the force per charge from a 9.00e-6 C charge on the charges above at 1m, 2m, and 3 m.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field E-field Applet Back-up applet: fieldshttps://phet.colorado.edu/en/simulation/charges-and- fields What observations can we make about E-fields? Source Charges and Test Charges? Superposition of E-fields?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field Test charge is a small positive charge to sample the E-Field Charge of test charge is small compared to source charges (source charges are the charges that generate the field) E-field vectors E-field is the force per charge E-field vectors points away from + charges E-field vectors point towards - charges E-field for point charges gets weaker as distance from source point charges increases For a point charge E = F e / q = [k Q q / r 2 ] / q = k Q / r 2

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Find the Electric Field Given the following forces that a positive test charge feels if placed at these three points, find the E-field vectors at these points.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Find the Electric Field Given the following forces that a positive test charge feels if placed at these three points, find the E-field vectors at these points. How would the Force vectors and E-field vectors change at point 3 for the following changes: Replace the positive test charge (+q) with a negative test charge (-q) Replace the positive test charge (+q) with a test charge twice as large (+2q)

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Coulomb Force Problems 1.Sum of Electric Forces from Point Charges 2.Levitation 3.Static Equilibrium 4.Comparing Electric Forces and Gravitational Forces

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Electric Field Slide 20-34

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Electric Field of a Point Charge Slide 20-35

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Positive charges create an electric field in the space around them. In which case is the field at the black dot the smallest? Checking Understanding Slide 20-36

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. All charges in the diagram below are of equal magnitude. In each of the four cases below, two charges lie along a line, and we consider the electric field due to these two charges at a point along this line represented by the black dot. In which of the cases below is the net field to the right? Slide Checking Understanding

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. All charges in the diagram below are of equal magnitude. In each of the four cases below, two charges lie along a line, and we consider the electric field due to these two charges at a point along this line represented by the black dot. In which case is the magnitude of the field at the black dot the largest? Slide Checking Understanding

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Are the Fields Real??? Are either or both of these a possible electric field? Explain the reasoning behind your answer (Focus on the vectors, not the source charges)

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 1.Determine the magnitude and the direction of the electric field at point A. E-field Superposition Example In your physical diagram, make sure you label your r’s as well as your angles

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 1.Determine the magnitude and the direction of the electric field at point A. 2.Determine the individual forces and the net force on charge B for each of the following cases. Slide E-field Superposition Examples

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Field Vectors and Electric Field Lines E-field Applet 2 What observations can we make about E-field lines?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dipole and Uniform Electric Fields Slide 20-45

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Field Lines Slide 20-50

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A set of electric field lines is directed as below. At which of the noted points is the magnitude of the field the greatest? Slide Checking Understanding

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field Vectors Test charge is a small positive charge to sample the E-Field Charge of test charge is small compared to source charges (source charges are the charges that generate the E-field) E-field vectors E-field is the force per charge E-field vectors points away from + charges E-field vectors point towards - charges E-field for point charges gets weaker as distance from source point charges increases E-fields add as vectors, at a point in space E net,x = E 1x + E 2x + … For a point charge E = F e / |q| = [k |Q| |q t | / r 2 ] / |q t | = k |Q| / r 2 Electric Force

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field Lines E-Field lines start on + charges and end on -- charges Larger charges will have more field lines going out/coming in Density of Field lines is a measure of field strength – the higher the density the stronger the field The E-field vector at a point in space is tangent to the field line at that point. If there is no field line, extrapolate

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Conductors and Electric Fields Slide 20-55