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The Electric Field (Chapter 22.1-5) A. Meaning of Electric Field? Consider Coulomb’s Law describing force between charges q1 and q2 separated by distance r: F k q1 q 2 r2 Why does q2 ‘feel’ force? Can think of it as q1 setting up a ‘force field’ that q2 has entered The field is there irrespective of the presence of q2 The field exerts a force per charge on a charge q2 that enters it. kq F 21 r̂ , where we are assuming q1 is a point charge, and r̂ is unit vector q2 r pointing away from q1. Thus E Electric field is a vector field, i.e., a region of space that has vectors associated with each location. The direction of the vector is the direction of force a positive test charge would experience at that location. The magnitude of the vector is the force/per charge a test charge would experience at that location. (Discuss similarities to the gravitational field) B. Visualizing Electric Fields Represented visually different ways Electric field lines (see figures 22-2b to 22-5 on pages 582 and 583) Electric field vectors (see figure 22-6 on page 584) Electric Field vectors C. Electric Fields of Simple Charge Configurations Electric field due to a point charge, q1, is given as in the above: E F kq1 2 rˆ q2 r If there is more than one source, we must do vector addition to get net field due to all sources, treating each source as a point source. Example: Like Problem 12, page 598 Calculate the direction and magnitude of the electric field at point P due to the three point charges. +q +q X P a +2q a P X a +q +2q a +q The E-field contributions by the +q charges cancel each other out. The magnitude of the contribution to the E-field by the +2q charge is: E k q1 r 2 k ( 2q ) 1 a2 a2 2 2 2kq 4kq 2 1 2 a a 2 The direction is given by the remaining arrow pointing to the upper right. Visualizing Three Special Cases: Two positive charges Two negative charges One positive and one negative charge D. Electric Field due to Electric Dipole Special case of E at distance z from electric dipole Assumes z >> d E kqd kp 3 where p is electric dipole moment z3 z (see pages 585-587 for development) z + d - E. Electric Fields and Conductors Charge a conductor. How does the charge distribute itself? Sphere Spherical shell Arbitrary solid shape What is the electric field like inside a charged conductor? How do electric field lines ‘meet’ a conductor?