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Chapter 20 Electric Forces and Fields Topics: • Electric charge • Forces between charged • • objects The field model and the electric field Forces and torques on charged objects in electric fields Sample question: In electrophoresis, what force causes DNA fragments to migrate through the gel? How can an investigator adjust the migration rate? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field Superposition Example 1. Determine the magnitude and the direction of the electric field at point A. 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. 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 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 Enet,x = E1x + E2x + … • For a point charge E = Fe / |q| = [k |Q| |qt| / r2] / |qt| = k |Q| / r2 • 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. Electric Field Lines Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Additional Clicker Questions A small sphere is suspended from a string in a uniform electric field. Several different cases of sphere mass and sphere charge are presented in the following table. In which case is the angle at which the sphere hangs the largest? Sphere mass (g) A. 2.0 B. 3.0 C. 2.0 D. 3.0 E. 4.0 Sphere charge (nC) 4.0 4.0 6.0 8.0 9.0 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer A small sphere is suspended from a string in a uniform electric field. Several different cases of sphere mass and sphere charge are presented in the following table. In which case is the angle at which the sphere hangs the largest? Sphere mass (g) C. 2.0 Sphere charge (nC) 6.0 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field Worksheet 2 Problem 7 a. Sketch the electric field created by the group of positive source charges shown below (ignore test charges A, B, and C for the moment.) Use arrows on field lines to show the direction of the field. b. Test charge particles A, B, and C are shot to the right. Predict and draw the path each particle will take. c. Where in the electric field will the particle’s paths be bent the most? test charges Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. source charges Consider an infinite sheet of charge • What kind of symmetry would we expect? • What will the field look like? • Is the field (A) converging, (B) diverging, or (C) neither -- (D) can’t tell • What can we say about E-field strength? • A charged sheet can be considered to be like an infinite sheet when we look at points a distance d away where d << L, where L is the length of a side of the sheet Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Consider an infinite sheet of charge h Q E= where h = 2e 0 A • Epsilon nought, e 0 = 8.85 ´ 10 -12 C2 N × m2 is electric permitivity of free space • Electric permitivity is a measure of how well electric field can pass through space or material Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Consider two infinite sheets of charge What is the E-field at points A, B, and C ? A B Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. C E-field Symmetry Cases Sphere Long Wire Plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Two parallel plates have charges of equal magnitude but opposite sign. What change could be made to increase the field strength between the plates? A. B. C. D. E. Increase the magnitude of the charge on both plates Decrease the magnitude of the charge on both plates Increase the distance between the plates Decrease the distance between the plates Increase the area of the plates (while keeping the magnitude of the charges the same) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer Two parallel plates have charges of equal magnitude but opposite sign. What change could be made to increase the field strength between the plates? A. B. C. D. E. Increase the magnitude of the charge on both plates Decrease the magnitude of the charge on both plates Increase the distance between the plates Decrease the distance between the plates Increase the area of the plates (while keeping the magnitude of the charges the same) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.