Electrical Fields


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Electrical Fields

  1. 1. Electrical Fields February 24th, 2009
  2. 2. Electric Field Strength <ul><li>Electric Field </li></ul><ul><ul><li>Region in space around a charged object in which a stationary charged object experiences an electric force because of its charge </li></ul></ul><ul><ul><li>Depends on Charge and distance </li></ul></ul><ul><ul><li>E = F electric / q 0 (see p. 643 in book) </li></ul></ul><ul><ul><li>Substitute in for F electric (see p. 644) </li></ul></ul><ul><ul><li>E = k c (q/r 2 ) </li></ul></ul>
  3. 3. <ul><li>Example </li></ul><ul><ul><li>An electrical field around a charged object is 5.95 x 10 6 N/C at a distance of 10.0 cm. Find the charge on the object </li></ul></ul>
  4. 4. Electric Field Lines <ul><li>Lines that represent both the magnitude and direction of the electric field </li></ul><ul><li>Number of lines is proportional to the electric field strength (more lines = stronger) </li></ul>
  5. 5. Rules for Drawing <ul><li>Line must begin at positive charge (or infinity) and must end at negative charge (or infinity) </li></ul><ul><li>Number of lines is proportional to magnitude of the charge </li></ul><ul><li>No two field lines from the same field can cross each other </li></ul>
  6. 6. Field Strength <ul><li>Field strength decreases as you move away from a charged object </li></ul>
  7. 7. Field Drawing with Two Charges <ul><li>Since forces are vectors the field strength is just the vector sum of both fields </li></ul>
  8. 8. More Examples
  9. 9. Unequal Charges <ul><li>Can determine ratio of charge by seeing how many lines terminate </li></ul>
  10. 10. Electric Field Practice Problems <ul><li>Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? _________ Explain what is wrong with all incorrect diagrams. </li></ul><ul><li>Answer: C, D and E </li></ul><ul><li>In C, the lines are directed towards a positively charged object. </li></ul><ul><li>In D, the lines are not symmetrically positioned despite the fact </li></ul><ul><li>that the object is a symmetrical sphere. </li></ul><ul><li>In E, the lines are directed away from a negative charge. </li></ul>
  11. 11. <ul><li>Erin Agin drew the following electric field lines for a configuration of two charges. What did Erin do wrong? Explain. </li></ul><ul><li>Electric field lines should never intersect each other. Erin crossed his lines. </li></ul>
  12. 12. <ul><li>Consider the electric field lines shown in the diagram below. From the diagram, it is apparent that object A is ____ and object B is ____. </li></ul><ul><li>Electric field lines are directed towards object A so object A must be negative. They are directed away from object B so object B must be positive. </li></ul>
  13. 13. <ul><li>Consider the electric field lines drawn at the right for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest. </li></ul><ul><li>Answer: DAECB (with the order of C and B being in question) </li></ul><ul><li>Electric field strength is greatest where the lines are closest together and weakest where lines are furthest apart. </li></ul>
  14. 14. <ul><li>Use your understanding of electric field lines to identify the charges on the objects in the following configurations. </li></ul><ul><li>Answer: Objects A, C, F, G, H and I are positive. </li></ul><ul><li>Objects B, D and E are negatively charged. The principle is: electric field lines always approach negatively charged objects and are directed away from positively charged objects. </li></ul>
  15. 15. <ul><li>Observe the electric field lines below for various configurations. Rank the objects according to which has the greatest magnitude of electric charge, beginning with the smallest charge. </li></ul><ul><li>Answer: B < A C < D G < E < F J < H < I </li></ul><ul><li>The principle is that objects with the greatest charge will have the greatest number of lines emanating from it or approaching it. </li></ul>
  16. 16. Resultant Force <ul><li>When more than two charges are present often it is necessary to find the net electric force on one of them </li></ul><ul><li>Coulomb’s law applies even when more than two charges are present </li></ul><ul><li>Just find the forces acting on each charge and add (or subtract) </li></ul><ul><li>This is the Principle of Superposition </li></ul>
  17. 17. Example <ul><li>Three charges are located on the x-axis. A 5.0  C charge is located at x=0.0 cm, a 1.5  C charge is located at x=3.0 cm and a -3.0  C charge is located at x=5.0 cm. Find the resultant force on the 5.0  C charge </li></ul><ul><li>21N </li></ul>
  18. 18. Practice <ul><li>Three charges are placed in a line: </li></ul><ul><li>Find the net force on all three charges </li></ul>A B C -5 C -8 C 2 C 2 m 5 m
  19. 19. Conductors in Electrostatic Equilibrium <ul><li>Electrostatic equilibrium </li></ul><ul><ul><li>When no net motion of charge is occurring within a conductor </li></ul></ul><ul><ul><ul><li>Electrical field is 0 everywhere inside conductor </li></ul></ul></ul><ul><ul><ul><li>Any excess charge resides entirely on the conductors outer surface </li></ul></ul></ul><ul><ul><ul><li>Electrical field just outside a charge conductor is perpendicular to the conductor’s surface </li></ul></ul></ul><ul><ul><ul><li>Charge tends to accumulate where the radius of curvature of the surface is smallest (sharp points) </li></ul></ul></ul>