Physics 122 B Electricity and Magnetism Lecture 8

Physics 122 B Electricity and Magnetism Lecture 8 (Knight: 28. 1 to 28. 5) Review of Material to be examined in Midterm 1 Current and Resistance April 11, 2007 Martin Savage Physics 122 B - Lecture 8

Lecture 8 Announcements l. The Midterm examination is this Friday during lecture time. You should bring with you to the Exam a good calculator, a Scantron sheet, and one sheet of 8. 5”x 11” paper on which you have written anything you wish on both sides. l. No cell phones or wireless communication allowed. l Lecture HW Assignment #3 will be been posted on Tycho and is due at 10 PM on Wednesday, April 18 9/17/2020 Physics 122 B - Lecture 8 2

Summaries Knight, Chapters 25, 26 and 27 Physics 122 B - Lecture 8

Summary: Chapter 25 (1) 9/17/2020 Physics 122 B - Lecture 8 4

Summary: Chapter 25 (2) Charges Fields Not really true… semi-conductors Not always true… Only if object is polarizable 9/17/2020 Physics 122 B - Lecture 8 5

Chapter 26 Summary (1) The E field exists at each point in space Non-zero values of the E-field are induced by electric charges 9/17/2020 Physics 122 B - Lecture 8 6

Chapter 26 Summary (2) 9/17/2020 Physics 122 B - Lecture 8 7

Chapter 27 Summary (1) 9/17/2020 Physics 122 B - Lecture 8 8

Chapter 27 Summary (2) 9/17/2020 Physics 122 B - Lecture 8 9

Chapter 27 Summary (3) 9/17/2020 Physics 122 B - Lecture 8 10

The Electron Current We start with some “thought experiments” on a simple system. We have a parallel plate capacitor that has been charged, e. g. with glass and plastic rods. Now we connect the plates with a wire. What happens? The plates quickly become neutral, and we say that the capacitor has been discharged. Further study shows that while the discharge is taking place, the wire gets warm, a light bulb can be made to glow, and a compass needle can be deflected. These are indicators of current flow in the wire. 9/17/2020 Physics 122 B - Lecture 8 11

Charge Carriers and Inertia Does the discharge occur because positive charges are moving to the negative plate, or because negative charges are moving to the positive plate? We have asserted that the current in metals is caused by the flow of negative electrons. The first direct evidence that this was the case was provided in 1916 by the Tolman-Stewart experiment, which showed that negative charges “go to the bottom” of an accelerated conductor. We model a metallic conductor as a rigid lattice of positive charges pervaded by a “sea” of conduction electrons, 1 per atom, that move freely in the material. 9/17/2020 Physics 122 B - Lecture 8 + + - - - + + - - + + 12

The Electron Current - In a metallic conductor in electrostatic equilibrium, the conduction electrons move around quite rapidly, but there is no net movement of charge. This can be changed by “pushing” on the sea of electrons with an electric field, thereby causing the entire sea of electrons to move in a particular direction, like a gas or liquid flowing through a pipe. The net motion, the “drift speed” vd, is superposed on the random thermal motions of the individual electrons, and it is very slow, typically around 10 -4 m/s. 9/17/2020 - We define the electron current i as the number of electrons Ne that pass through a cross section of wire or other conductor in a time interval Dt. In other words: Ne = i Dt. Physics 122 B - Lecture 8 13

Current and Drift Velocity If the electrons have an average drift speed vd, then on the average in a time interval Dt they would travel a distance Dx in the wire, where Dx = vd Dt. If the wire has cross sectional area A and there are n electrons per unit volume in the wire, then the number of electrons moving through the cross sectional area in time Dt is Ne = n A Dx = n A vd Dt = i Dt. Therefore, 9/17/2020 Physics 122 B - Lecture 8 This table gives n for various metals. 14

Question 1 Which wire has the largest electron current? 9/17/2020 Physics 122 B - Lecture 8 15

Conservation of Current Question: An electron current i. A flows to the light bulb, passing point A, where it delivers some energy and makes the bulb glow. How much electron current i. B then passes point B? Answer: All of it! i. A=i. B. Reason: the electrons don’t have anywhere else to go. What goes to the bulb must return from the bulb. The bulb cannot “use up” the electrons. Plumber’s Analogy 1: If water flows into a constant diameter pipe at 2. 0 m/s, it must flow out of the pipe at the same speed. It cannot “pile up” in the pipe. This principle is called “Conservation of Current”. 9/17/2020 Physics 122 B - Lecture 8 16

A Puzzle We discharge a capacitor that has been given a charge of Q = 16 n. C, using a copper wire that is 2 mm in diameter and has a length of L = 20 cm. Assume that the electron drift speed is vd = 10 -4 m/s. How long does it take to discharge the capacitor? (Note that L/vd = 0. 2 m/10 -4 m/s = 2000 s = 33. 3 min. ) Points to consider: 1. The wire is already full of electrons. 2. The wire contains about 5 x 1022 conduction electrons. 3. Q = 16 n. C requires about 1011 electrons. 4. A length L’ of wire that holds 16 n. C of conduction electrons is 4 x 10 -13 m. 5. L’/vd = 4 x 10 -9 s = 4 ns. That is roughly the discharge time. 9/17/2020 Physics 122 B - Lecture 8 17

Creating a Current… Non-Static Situation Suppose you want to slide a book across a table. If you give it a quick push, it moves but slows due to friction as soon as you remove your hand, and its kinetic energy becomes heat. The only way to make the book move at a constant speed is to continue pushing it. The sea of conduction electrons is similar to the book. If you push the electrons, you create a current, but they are not moving in vacuum, and collisions with other electrons and atoms soon dissipates their kinetic energy as heat. The only way to maintain the current of electrons is to push them, using an electric field. An electron current is a non-equilibrium motion in an E field. 9/17/2020 Physics 122 B - Lecture 8 18

Establishing the Electric Field in a Wire (1) The figure shows two metal wires attached to the plates of a parallel plate capacitor, with their ends close together but not touching. The wires are conductors, so some of the charge from the capacitor plates spreads out along the wires as surface charge. E=0 inside all conductors. . plates and wires. Now we connect the wires. What happens? The surface electrons can move, and do so. In ~10 -9 s the sea of electrons shifts slightly, and the surface charges are rearranged into a non-uniform distribution of charges, as shown. Surface charges near the + and – plates reflect these charges, but surface charges become near-neutral halfway along the wire 9/17/2020 Physics 122 B - Lecture 8 19

Establishing the Electric Field in a Wire (2) The figure shows the region of the wire near the neutral midpoint. The surface charge rings become more positive to the left and more negative to the right. In Chapter 26, we found that a ring of charge makes an on-axis E field that: 1. Points away from a positive ring and toward a negative ring; 2. Is proportional to the net charge of the ring; 3. Decreases with distance from the ring. The non-uniform surface charge distribution creates an E field inside the wire. This pushes the electron current through the wire 9/17/2020 Physics 122 B - Lecture 8 20

Example: The Surface Charge on a Current-Carrying Wire Two 2. 0 mm diameter charged rings, with charges ±Q, are 2. 0 mm apart. What value of Q causes the electric field at the midpoint to be E=0. 010 N/C? 9/17/2020 Physics 122 B - Lecture 8 21

Turning the Corner 9/17/2020 Physics 122 B - Lecture 8 22

Question 2 Which surface charge distribution will produce the largest electron current? 9/17/2020 Physics 122 B - Lecture 8 23

A Model of Conduction (1) 9/17/2020 Now turn on an E field. The straight-line trajectories become parabolic, and because of the curvature, the electrons begin to drift in the direction opposite E, i. e. , “downhill”. ax=F/m=e. E/m so vx=vix+ ax. Dt = vix+ Dt e. E/m This acceleration increases an electrons kinetic energy until the next collision, a “friction” that heats the wire…. energy is imparted to the atoms of the lattice. Physics 122 B - Lecture 8 24

A Model of Conduction (2) One Collision Time-History over many Collisions Collision is independent of E 9/17/2020 Physics 122 B - Lecture 8 25

Example: The Electron Current in a Copper Wire The mean time between collisions for electrons in room-temperature copper is t = 2. 5 x 10 -14 s. What is the electron current in 2. 0 mm diameter copper wire where the internal field strength is E = 0. 010 N/C? 9/17/2020 Physics 122 B - Lecture 8 26

Batteries and Current 9/17/2020 Physics 122 B - Lecture 8 27

Electrical Current D D 9/17/2020 Physics 122 B - Lecture 8 28

Example: The Current in a Copper Wire From the previous example, What is the current I? How much charge passes through the wire in an hour? D 9/17/2020 Physics 122 B - Lecture 8 29

Current and Electrons 9/17/2020 Physics 122 B - Lecture 8 30

The Current Density in a Wire Example: A current of 1. 0 A passes through a 1. 0 mm diameter aluminum wire. What is the drift speed of the electrons in the wire? 9/17/2020 Physics 122 B - Lecture 8 31

End of Lecture 8 l Before the next lecture, read Knight: 29. 1 to 29. 4. l Exam Friday…. study everything in chaps 25, 26, 27 l Will NOT cover material on currents and non-static situations. 9/17/2020 Physics 122 B - Lecture 8 32