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1. Physics 122B Electricity and Magnetism Lecture 16 (Knight: 31.9,10 & 32.1) Grounding, RC Circuits, Magnetism May 7, 2007 Martin Savage

2. Lecture 17 Announcements • Lecture HW Assignment #5 has been posted on Tycho and is due at 10 PM on Wednesday. • Check Tycho for your exam scores. If there are missing parts, you may not have put your name on your paper. See Helen Gribble, C136 PAB, to fix such problems. Physics 122B - Lecture 17

3. Example:Analyzing a Complex Circuit (2) Physics 122B - Lecture 17

4. Maximum Power Transfer Question:For a battery with EMF E and internal resistance r, what value should an adjustable external load resistance R have to make the power dissipated in R as large as possible? I r R E PRis a maximum when r-R = 0 or r=R. In other words, energy can be drawn from the battery at the greatest rate when the external load resistance matches the internal resistance of the battery. This is called load matching. It is very important in transferring energy and signals with minimum loss. But note that only ½ of the energy gets to R. Physics 122B - Lecture 17

5. Grounding and GFI Modern power wiring includes a “ground” line, the round 3rd wire of an electrical plug. The ground point defines a point of zero potential, which is normally connected directly to the Earth (Vearth=0). The operation of any circuit depends only on potential differences, so it should not be affected by the presence or absence of a ground connection. Because the ground connection is connected at only one point, no current should flow through the ground connection. However, if some other part of a circuit is accidentally grounded, current is likely to flow through the ground line. GFI (ground fault interruption) circuits, widely used, e.g., in bathroom wiring, detect current flow in the ground line and interrupt power automatically when it occurs. This has prevented many accidental electrocutions. Physics 122B - Lecture 17

6. Light Fixture V=0 Physics 122B - Lecture 17

7. Example:A Grounded Circuit The circuit shown is grounded at the junction between the two resistors rather than at the bottom. Find the potential at each corner of the circuit. Physics 122B - Lecture 17

8. RC Circuits I = - dQ/dt Exponential decay! Physics 122B - Lecture 17

9. RC Exponential Decay Define RC time constant: tºRC I0º Q0/RC Physics 122B - Lecture 17

10. Charging Capacitors: Early and Late Initially, when a switch closes there is a potential difference of 0 V across an uncharged capacitor. After a long time, the capacitor reaches its maximum charge and there is no current flow through the capacitor. Therefore, at t=0 the capacitor behaves like a short circuit (R=0), and at t=∞ the capacitor behaves like at open circuit (R=∞). Example: 100 V 100 V 12.5 A 100 V 2.5 A 10 A 0 V at t=0 at t=∞ Circuit Calculate initial currents.IB = 100 V/8 W = 12.5 A Calculate final potentials. Physics 122B - Lecture 17

11. Example: ExponentialDecay in a RC Circuit The switch has been in position ``a’’ for a long time. It is changed to position ``b’’ at t=0. What are the charge is the capacitor and the current through the resistor at t=5.0 ms? Physics 122B - Lecture 17

12. Charging a Capacitor Physics 122B - Lecture 17

13. Question The time constant for the discharge of the capacitor is: (a) 5 s; (b) 4 s; (c) 2 s; (d) 1 s; (e) the capacitor does not discharge because the resistors cancel. Physics 122B - Lecture 17

14. Plumber’s RC Analogy* Valve Constriction P1 P2 RubberDiaphragm Pump The “plumber’s analogy” of an RC circuit is a pump (=battery) pumping water in a closed loop of pipe that includes a valve (=switch), a constriction (=resistor), and a rubber diaphragm. When the valve starts the flow, the diaphragm stretches until the pressure difference across the pump (P1-P3) equals that across the diaphragm (P2-P3). P3 Pump = Battery Valve = Switch Constriction = Resistor Capacitor= Rubber Diaphragm Pressure = PotentialWater Flow = Current Physics 122B - Lecture 17

15. Chapter 31 Summary (1) Physics 122B - Lecture 17

16. Chapter 31 Summary (2) Physics 122B - Lecture 17

17. Chapter 31 Summary (3) Physics 122B - Lecture 17

18. Experiments with Magnetism:Experiment 1 Tape a bar magnet to a cork and allow it to float in a dish of water. The magnet turns and aligns itself with the north-south direction. The end of the magnet that points north is called the magnet’s north-seeking pole, or simply its north pole. The other end is the south pole. Physics 122B - Lecture 17

19. Experiments with Magnetism:Experiment 2 Bring the north poles of two bar magnets near to each other. Then bring the north pole of one bar magnet near the south pole of another bar magnet. When the two north poles are brought near, a repulsive force between them is observed. When the a north and a south pole are brought near, an attractive force between them is observed. Physics 122B - Lecture 17

20. Experiments with Magnetism:Experiment 3 Bring the north pole of a bar magnet near a compass needle. When the north pole is brought near, the north-seeking pole of the compass needle points away from the magnet’s north pole. Apparently the compass needle is itself a little bar magnet. Physics 122B - Lecture 17

21. Experiments with Magnetism:Experiment 4 Use a hacksaw to cut a bar magnet in half. Can you isolate the north pole and the south pole on separate pieces? No. When the bar is cut in half two new (but weaker) bar magnets are formed, each with a north pole and a south pole. The same result would be found, even if the magnet was sub-divided down to the microscopic level. Physics 122B - Lecture 17

22. Experiments with Magnetism:Experiment 5 Bring a bar magnet near an assortment of objects. Some of the objects, e.g. paper clips, will be attracted to the magnet. Other objects, e.g., glass beads, aluminum foil, copper tacks, will be unaffected. The objects that are attracted to the magnet are equally attracted by the north and south poles of the bar magnet Physics 122B - Lecture 17

23. Experiments with Magnetism:Experiment 6 Bring a magnet near the electrode of an electroscope. There is no observed effect, whether the electroscope is charged or discharged and whether the north or the south pole of the magnet is used. Physics 122B - Lecture 17

24. Conclusions from Experiments • Magnetism is not the same as electricity. Magnetic poles are similar to charges but have important differences. • Magnetism is a long range force. The compass needle responds to the bar magnet from some distance away. • Magnets have two poles, “north” (N) and “south” (S). Like poles repel and opposite poles attract. • Poles of a magnet can be identified with a compass. A north magnet pole (N) attracts the south-seeking end of the compass needle (which is a south pole). • Some materials (e.g., iron) stick to magnets and others do not. The materials that are attracted are called magnetic materials. Magnetic materials are attracted by either pole of a magnet. This is similar in some ways to the attraction of neutral objects by an electrically charged rod by induced polarization. Physics 122B - Lecture 17

25. Monopoles and Dipoles Every magnet that has ever been observed is a magnetic dipole, containing separated north and south poles. Attempts to isolate one pole from the other fail. It is theoretically possible to have magnetic monopoles, i.e., isolated magnetic poles with a “north” or “south” magnetic charge. Search have been conducted, but no such object has ever been found in nature. For the purposes of this course, we will assume that isolated magnetic monopoles do not exist, but we will point out the places in the formalism where they would go if they did exist. Physics 122B - Lecture 17

26. Lecture 17 Announcements • Lecture HW Assignment #5 has been posted on Tycho and is due at 10 PM on Wednesday. • Check Tycho for your exam scores. If there are missing parts, you may not have put your name on your paper. See Helen Gribble, C136 PAB, to fix such problems. Physics 122B - Lecture 17