# L:ec 7

## Physics 208 with Carlsmith at University of Wisconsin - Madison *

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electric fields are responsible for the electric currents that flow through your computer and the nerves in your body. Electric fields also line up polymer molecules to form the images in a liquid crystal display (LCD). Chapter Goal: To learn how to calculate and use the electric field. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electric field at a point in space r of a point charge q at the origin, r = 0, is the force per unit charge placed at r: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. Up. B. Down. C. Left. D. Right. E. The electric field is zero. At the position of the dot, the electric field points Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. Up. B. Down. C. Left. D. Right. E. The electric field is zero. At the position of the dot, the electric field points Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electric field exerts a force In a uniform field, the acceleration is: on a charged particle. If this is the only force acting on q, it causes the charged particle to accelerate with Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The net electric field due to a group of point charges is where E i is the field from point charge i. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 7 Which vector best represents the electric field at the red dot? - A B C D E - Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 8 Which vector best represents the electric field at the red dot? A B C - D E - Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. For two opposite charges ±q separated by the small distance s, the dipole moment is defined as the vector An effective dipole-moment vector characterizes the distant electric field of any neutral charge distribution. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 10 On the y-axis s/2 −s/2 x y E=E y ˆ y E y =E + E − ≈k2qs ( ) 1 y 3 for y>>s Since points from - charge to + charge p E =k 2 p r 3 on y-axis of dipole only s q -q =kq 1 y−s/2 ( ) 2 +−kq ( ) 1 y+s/2 ( ) 2 =kq 2ys y−s/2 ( ) 2 y+s/2 ( ) 2 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electric field at a point on the axis of a dipole is where r is the distance measured from the center of the dipole. (A net charge atop the dipole would add a 1/r^2 term.) The electric field in the plane that bisects and is perpendicular to the dipole is This field is opposite to the dipole direction, and it is only half the strength of the on-axis field at the same distance. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. In a uniform electric field, the net force on a dipole vanishes but the net torque need not. The torque on a dipole in an electric field is where θ is the angle the dipole makes with the electric field. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electric field lines follow the flow and help visualize the field. (Thanks Faraday!) Field lines are tangent to the electric field and never cross. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Random vector representation Field line representation Notice the density of lines corresponds to field strength. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. You can almost “see” the repulsion in the field lines. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Water is a polar molecule, neutral but with charged legs. Those charges enable it to rip apart (dissolve) other molecules. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. We can describe a smoothly varying charge distribution in terms of a charge density function ala’ mass density. For example, the linear charge density of an object of length L and charge Q uniformly distributed along its length , is defined as Linear charge density, which has units of C/m, is the amount of charge per meter of length. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. We can calculate the electric field of a general charge distribution by dividing it into small pieces and summing the fields of the pieces using methods of calculus as the number of pieces tend to infinity. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A very long, thin rod or taut wire, with uniform linear charge density λ, has an electric field pointing radially away from the rod. where r is the radial distance (cylindrical coordinate) away from the rod. Except for the factor 2, this can be guessed by dimensional analysis. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The on-axis electric field of a charged disk of radius R, centered on the origin with axis parallel to z, and surface charge density η = Q/πR 2 is NOTE: The field for z < 0 has the same magnitude but points in the opposite direction. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electric field of an infinite plane with surface charge density η is: For a positively/negatively charged plane, the electric field points away from /towards the plane on both sides of the plane. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A sphere of charge Q and radius R, be it a uniformly charged sphere or just a spherical shell, has an electric field outside the sphere that is exactly the same as that of a point charge Q located at the center of the sphere: But inside a spherical shell of charge, the field vanishes. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. • The figure shows two electrodes, one with charge +Q and the other with –Q placed face-to-face a distance d apart. • This arrangement of two electrodes, charged equally but oppositely, is called a parallel-plate capacitor. • Capacitors play important roles in many electric circuits. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electric field inside a capacitor is where A is the surface area of each electrode. Outside the capacitor plates, where E + and E – have equal magnitudes but opposite directions, the electric field is zero. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. QUESTIONS: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. ++++++++++++ -------------------- E Do work to charge the capacitor thereby storing energy. Discharge capacitor through light bulb filament converting stored energy to heating the filament and to radiant energy (light, heat). Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electric force field of a collection of charges may be calculated using superposition and Coulomb’s Law. The electric field is cleverly visualized with field lines. Electronics concerns the deployment and redeployment of a vast number of electrons on conducting surfaces as in a capacitor serving as information carriers and sources of force field. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A piece of plastic is uniformly charged with surface charge density 1 . The plastic is then broken into a large piece with surface charge density 2 and a small piece with surface charge density 3 . Rank in order, from largest to smallest, the surface charge densities 1 to 3 . A. η 2 = η 3 > η 1 B. η 1 > η 2 > η 3 C. η 1 > η 2 = η 3 D. η 3 > η 2 > η 1 E. η 1 = η 2 = η 3 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A piece of plastic is uniformly charged with surface charge density 1 . The plastic is then broken into a large piece with surface charge density 2 and a small piece with surface charge density 3 . Rank in order, from largest to smallest, the surface charge densities 1 to 3 . A. η 2 = η 3 > η 1 B. η 1 > η 2 > η 3 C. η 1 > η 2 = η 3 D. η 3 > η 2 > η 1 E. η 1 = η 2 = η 3 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which of the following actions will increase the electric field strength at the position of the dot? A. Make the rod longer without changing the charge. B. Make the rod fatter without changing the charge. C. Make the rod shorter without changing the charge. D. Remove charge from the rod. E. Make the rod narrower without changing the charge. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which of the following actions will increase the electric field strength at the position of the dot? A. Make the rod longer without changing the charge. B. Make the rod fatter without changing the charge. C. Make the rod shorter without changing the charge. D. Remove charge from the rod. E. Make the rod narrower without changing the charge. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Rank in order, from largest to smallest, the forces F a to F e a proton would experience if placed at points a – e in this parallel-plate capacitor. A. F a = F b = F d = F e > F c B. F a = F b > F c > F d = F e C. F a = F b = F c = F d = F e D. F e = F d > F c > F a = F b E. F e > F d > F c > F b > F a Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. F a = F b = F d = F e > F c B. F a = F b > F c > F d = F e C. F a = F b = F c = F d = F e D. F e = F d > F c > F a = F b E. F e > F d > F c > F b > F a Rank in order, from largest to smallest, the forces F a to F e a proton would experience if placed at points a – e in this parallel-plate capacitor. duncan lect7.pdf

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