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PHYS 1110 Lecture 5 Professor Stephen Thornton September 13, 2012 Reading Quiz metal conductor (rod and sphere are not touching) A metal conductor has been sitting for a very long time. We bring up a negatively charged rod, close to, but not touching the conductor. Which of the following is most true about this diagram? A) The diagram is wrong, because charge is not conserved. B) The diagram looks okay. C) The diagram is wrong, because the charge configuration is unlikely. Answer: C A is not correct, because charges do not have to be conserved. There was charge on the Teflon rod. C is correct, because the negative charge on the conductor would be repelled by the negative charge on the rod and move away. Rub a Teflon rod on fur. See what happens. Try to pick up pieces of paper. When we rub one item on another, electrons are rubbed off one item to the other. Discuss atomic model. Rabbit fur ++++++ Glass +++++ Human hair ++++ Nylon +++ Silk ++ Paper + Cotton - Wood -- Amber --- Rubber ---- PVC ----- Teflon ------ Electrical Polarization Polar molecules (water H2O, ammonia NH3, hydrogen fluoride HF) Look at demo: 2 x 4 on watch glass. How does Teflon rod cause board to move? Benjamin Franklin is the one who named the charges positive and negative. We now know the electrons (which are mobile and carry charge) are negative. Law of conservation of charge: the net amount of charge is conserved in any process. We are dealing with Electrostatics- charges at rest. Conductors are materials that conduct charge easily. Examples are metals like aluminum, copper, iron, etc. Insulators are materials that do not conduct charge easily. Examples are glass, plastics, ceramics (nonmetallic). Semiconductors are materials that are between conductors and insulators and can conduct charge under special conditions like at high temperatures. What about water and air? Water is a polar molecule. Air is mostly N 2 , O 2 , not easily polarized. Look at this You Tube video for the dangers of electrostatics. Let’s consider some experiments and see what happens. 1) Like charges repel and unlike charges attract. 2) If we vary the distance between point charges, we find the force becomes smaller as the separation distance 1 increases. F r2 3) If we vary the charge magnitude, we find F ~ q1q2 4) Put these results together and obtain the Coulomb force. kq1q2 1 F 2 where k 8.99 10 r 4 0 9 Nm / C 2 2 Forces Between Point Charges kq1q2 F12 2 êr r F12 is force on 1 due to 2. Superposition of Forces qq F 1 2 êr 12 4 r 2 0 We find the total force by adding the vector sum of the individual forces. Conceptual Quiz A Conceptual Quiz B C Which of the arrows best D represents the direction of the net force on charge d +2Q +Q +Q due to the other two charges? d +4Q E A Conceptual Quiz B C Which of the arrows best D represents the direction of the net force on charge d +2Q +Q +Q due to the other two d charges? +4Q The charge +2Q repels +Q toward the right. The charge +4Q repels +Q upward, but with a stronger force. Therefore, the net force is up and to +2Q the right, but mostly up. Follow-up: What would happen if the yellow charge were +3Q? +4Q E Electric field What is a field? Why do we want to learn about them? Discuss fields in general temperature (use thermometer) gravitation (use test mass) pressure (weather maps) An Electrostatic Force Field Use a small test charge q0 to find force due to charge +q. q0 Definition of Electric Field qq F k 20 r F is force between charge q and test charge q0 (small). The test charge is used to map out the electric field due to charge q. F kq E = 2 eˆ r Electric field due to a charge q0 r q (not q0 ). Unit: N/C Electric Field of a Point Charge F kq E = 2 eˆ r q0 r E k q2 r k 1 4 0 The Direction of the Electric Field for Point Charges Superposition of the Electric Field q2 E2 k 2 d q1 E1 k 2 d Imagine the test charge could be placed here. The test charge is only useful to imagine the force field. Relation between F and E If we put a charge q1 in an electric field E , then the charge q1 feels a force of value F1 q1E This is the really useful part. Don’t confuse this charge q1 with the test charge q0 or the original charges q that produced E. The test charge q0 was used to find the electric field. This is a real charge q1 placed in the electric field. Determining electric fields Rules and hints: 1) E lines start on + charges, end on – charges. Can start and stop at infinity. 2) Place test charge q0 at any point and find direction of force on q0 to determine E line. 3) E lines can never intersect! 4) E lines are more dense when magnitude is greater. Electric Field Lines for a Point Charge Electric Field Lines for Systems of Charges We call this a dipole. It is a dipole field. Conceptual Quiz Which of the charges has the greater magnitude? A) B) C) both the same Conceptual Quiz Which of the charges has the greater magnitude? The field lines are denser around the red charge, so the red one has the greater magnitude. Follow-up: What is the red/green ratio of magnitudes for the two charges? A) B) C) both the same The Electric Field of a Charged Plate E 2 0 s is charge per unit area of plate Parallel charged plates Correct Charge Distribution on a Conducting Sphere If charges were inside the sphere, they would repel each other. Also E must be zero inside conductor or free electrons would move. Wrong Charges placed on a metal conductor must reside on the surface. The electric field near a conducting surface must be perpendicular to the surface when in equilibrium. If we place conductor in electric field, the E lines must be to surface. If not, charges would move. E must be zero inside. F q0 E W F s work U W qE s Ignore gravity Where does this electric field come from? The charge q0 feels a force due to E. The electric field E does work on the charge. The charge has a higher potential energy on the left than it does on the right. The charge gains kinetic energy in the electric field. Change in Electric Potential Energy Who (or what) is doing work here? Change in Electric Potential Energy Electric field Gravitational field Who (or what) is doing work here? Electric Potential V U W V q0 q0 Unit: J/C = volt, V definition!! Electric potential, or potential, is one of the most useful concepts in electromagnetism. This is a biggie!! (notice that it has its own unit!) Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative – potential energy can be defined. Change in electric potential energy is negative of work done by electric force: U b - U a = - W = - qEd The electric field does work to move the positive charge q from a to b. Copyright © 2009 Pearson Education, Inc. Electric potential can be thought of as potential energy per unit charge: Ua Va = q DU DV = q It is really only the change in electric potential that is important, and we define it that way. Only changes in electric potential (or simply called potential) can be measured, allowing free assignment of V = 0. For example, we can let one of the voltages be zero at infinity. Copyright © 2009 Pearson Education, Inc. Electrical sources such as batteries and generators supply a constant potential difference. Here are some typical potential differences, both natural and manufactured: Copyright © 2009 Pearson Education, Inc. Energy conservation Energy conservation relations are still valid. K A U A KB U B If we look at definition of V , U we have V , so U qV q K B K A U A U B q (VA VB ) The change in kinetic energy is proportional to the change in electric potential!! Notes on electric potential kq Point charge V r Scalar quantity, not vector like electric field. For multiple charges, we simply add the potentials from each charge for simple superposition! In practice, we use potential concept much more than electric field. We can measure potential easily, but not electric field. Electric Potential Energy Electric potential energy for two point charges, q and q0, separated by a distance r, is simply q0 q U q0V k r Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the – plate. Which particle has the greatest kinetic energy when it reaches the other plate? A) proton B) electron C) the kinetic energies are the same. Answer: C The particles experience the same electric field and have the same charge. The kinetic energy increase is equal to the work done by the electric field. W = Fd = qEd Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the – plate. Which particle has the greatest speed when it reaches the other plate? A) proton B) electron C) the speeds are the same. Answer: B We just saw that the proton and electron will have the same kinetic energy increase. But K = mv2/2, and because the electron has such a smaller mass, its velocity must be much greater than that of the proton. Conceptual Quiz A At which point E) all of them does V = 0? B +Q C D kq V r –Q Conceptual Quiz A E) all of them At which point does V = 0? B +Q C –Q D All of the points are equidistant from both charges. Since the charges are equal and opposite, their contributions to the potential cancel out everywhere along the mid-plane between the charges. Follow-up: What is the direction of the electric field at all 4 points? Equipotential Surfaces kq V= r An equipotential is a line or surface over which the potential is constant. Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential. Copyright © 2009 Pearson Education, Inc. Equipotential Surfaces The electric field does no work by moving a charge perpendicular to the electric field, which is along the equipotential! Another case showing electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential. Copyright © 2009 Pearson Education, Inc. Electrostatic precipitators- demo Capacitance Simplest capacitor – two equal and oppositely charged conductors Parallel-plate capacitor: A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge. When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage: Q = CV The quantity C is a constant called capacitance. Copyright © 2009 Pearson Education, Inc. Capacitance If Q = CV, Q C V C 1F = 1 V C Unit: = farad or F V Parallel plate capacitor Q d V Ed d A 0 0 Q 0 A So V d and Q 0 A C d V The capacitance value depends only on geometry! Dielectric Effect of a Dielectric on the Electric Field of a Capacitor E E0 E E0 / and V V0 / where is the dielectric constant The induced electric field reduces the overall field: • Dielectric = insulator • Molecules act as dipoles, permanent or induced • This effectively reduces the electric field A dielectric is an insulator, and is characterized by a dielectric constant k . Capacitance of a parallel-plate capacitor filled with dielectric: C 0 A d C C0 for parallel-plate capacitor Using the dielectric constant, we define the permittivity: 0 Copyright © 2009 Pearson Education, Inc. Dielectrics Dielectric strength is the maximum electric field a dielectric can experience without breaking down. Copyright © 2009 Pearson Education, Inc. Energy Required to Charge a Capacitor Move charge D Q across plates. It takes work W and increases U. U W V Q Sum over the Q 2 Q 1 1 2 U QV CV 2C 2 2 Capacitor energy storage Electric Energy Storage Energy stored in a capacitor. Copyright © 2009 Pearson Education, Inc.