2. 2/26/2016 1 General Physics (PHY 2140) Lecture 11  Electricity and Magnetism Direct current circuits Kirchhoff’s rules RC circuits Magnetism Magnets Chapter 18-19

3. 2/26/2016 2 Last lecture: 1.DC circuits EMF EMF Resistors in series Resistors in series Resistors in parallel Resistors in parallel Review Problem: The circuit below consists of two identical light bulbs burning with equal brightness and a single 12 V battery. When the switch is closed, the brightness of bulb A 1. increases. 2. remains unchanged. 3. decreases.

4. The procedure for analyzing complex circuits is based on the principles of conservation of charge and energy They are formulated in terms of two Kirchhoff’s rules: 1. The sum of currents entering any junction must equal the sum of the currents leaving that junction (current or junction rule). 2. The sum of the potential differences across all the elements around any closed-circuit loop must be zero (voltage or loop rule). 2/26/2016 3

5. 4 The sum of the currents entering a node (junction point) equal to the sum of the currents leaving. 11 As a consequence of the Law of the conservation of charge, we have: Similar to the water flow in a pipe.

6. 1. Assign symbols and directions of currents in the loop – If the direction is chosen wrong, the current will come out with a right magnitude, but a negative sign (it’s ok). 2. Choose a direction (cw or ccw) for going around the loop. Record drops and rises of voltage according to this: – If a resistor is traversed in the direction of the current: -V = -IR – If a resistor is traversed in the direction opposite to the current: +V=+IR – If EMF is traversed “from – to + ”: + E – If EMF is traversed “from + to – ”: - E 2/26/2016 5 The sum of the potential differences across all the elements around any closed loop must be zero. 11 As a consequence of the Law of the conservation of energy, we have:

7. 2/26/2016 6 Loops can be chosen arbitrarily. For example, the circuit below contains a number of closed paths. Three have been selected for discussion. + + + ++ + + + + + + - - - - - - -- - - - v1v1 v2v2 v4v4 v3v3 v 12 v 11 v9v9 v8v8 v6v6 v5v5 v7v7 v 10 + - Path 1 Path 2 Path 3 Suppose that for each element, respective current flows from + to - signs.

8. 2/26/2016 7 + + + ++ + + + + + + - - - - - - -- - - - v1v1 v2v2 v4v4 v3v3 v 12 v 11 v9v9 v8v8 v6v6 v5v5 v7v7 v 10 + - “a” Blue path, starting at “a” - v 7 + v 10 – v 9 + v 8 = 0 “b” Red path, starting at “b” +v 2 – v 5 – v 6 – v 8 + v 9 – v 11 – v 12 + v 1 = 0 Yellow path, starting at “b” + v 2 – v 5 – v 6 – v 7 + v 10 – v 11 - v 12 + v 1 = 0 Using sum of the drops = 0

9. 2/26/2016 8 For the circuit below find I, V 1, V 2, V 3, V 4 and the power supplied by the 10 volt source. Example: For the circuit below find I, V 1, V 2, V 3, V 4 and the power supplied by the 10 volt source. 1.For convenience, we start at point “a” and sum voltage drops =0 in the direction of the current I. +10 – V 1 – 30 – V 3 + V 4 – 20 + V 2 = 0 (1) 2. We note that: V 1 = - 20I, V 2 = 40I, V 3 = - 15I, V 4 = 5I (2) 3. We substitute the above into Eq. 1 to obtain Eq. 3 below. 10 + 20I – 30 + 15I + 5I – 20 + 40I = 0 (3) Solving this equation gives, I = 0.5 A.

10. 2/26/2016 9 Using this value of I in Eq. 2 gives: V 1 = - 10 V V 2 = 20 V V 3 = - 7.5 V V 4 = 2.5 V P 10(supplied) = -10I = - 5 W (We use the minus sign in –10I because the current is entering the + terminal) In this case, power is being absorbed by the 10 volt supply.

11.  When switch is closed, current flows because capacitor is charging  As capacitor becomes charged, the current slows because the voltage across the resistor is  - V c and V c gradually approaches .  Once capacitor is charged the current is zero 2/26/2016 10 RC is called the time constant Charge across capacitor CECE 0.63 C E

12. If a capacitor is charged and the switch is closed, then current flows and the voltage on the capacitor gradually decreases. This leads to decreasing charge 2/26/2016 11 Charge across capacitor Q 0.37Q

13. 2/26/2016 12 A series combination of a 12 k  resistor and an unknown capacitor is connected to a 12 V battery. One second after the circuit is completed, the voltage across the capacitor is 10 V. Determine the capacitance of the capacitor.

14. 2/26/2016 13 A series combination of a 12 k  resistor and an unknown capacitor is connected to a 12 V battery. One second after the circuit is completed, the voltage across the capacitor is 10 V. Determine the capacitance of the capacitor. Given: R =12 k  E = 12 V V =10 V Find: C=? Recall that the charge is building up according to Thus the voltage across the capacitor changes as This is also true for voltage at t = 1s after the switch is closed, I R C

15. 2/26/2016 14

16.  Magnetic effects from natural magnets have been known for a long time. Recorded observations from the Greeks more than 2500 years ago.  The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece.  Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched.  Small sliver of lodestone suspended with a string will always align itself in a north-south direction—it detects the earth’s magnetic field.

17.  Bar magnet... two poles: N and S Like poles repel; Unlike poles attract.  Magnetic Field lines: (defined in same way as electric field lines, direction and density) Does this remind you of a similar case in electrostatics?

18. Magnetic Field Lines of a bar magnet Electric Field Lines of an Electric Dipole

19.  Perhaps there exist magnetic charges, just like electric charges. Such an entity would be called a magnetic monopole (having + or - magnetic charge).  How can you isolate this magnetic charge? Try cutting a bar magnet in half: Many searches for magnetic monopoles—the existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac)Many searches for magnetic monopoles—the existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac) No monopoles have ever been found!No monopoles have ever been found! NS NNSS Even an individual electron has a magnetic “dipole”!

20.  What is the source of magnetic fields, if not magnetic charge?  Answer: electric charge in motion! e.g., current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet.  Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter. Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect)

21. Electric Field: Distribution of charge creates an electric field E(r) in the surrounding space. Field exerts a force F=q E(r) on a charge q at r Magnetic Field: Moving charge or current creates a magnetic field B(r) in the surrounding space. Field exerts a force F on a charge moving q at r (emphasis this chapter is on force law) 2/26/2016 20

22. 2/26/2016 21 Materials can be classified by how they respond to an applied magnetic field, B app. Paramagnetic (aluminum, tungsten, oxygen,…) Atomic magnetic dipoles (~atomic bar magnets) tend to line up with the field, increasing it. But thermal motion randomizes their directions, so only a small effect persists: B ind ~ B app 10 -5 Diamagnetic (gold, copper, water,…) The applied field induces an opposing field; again, this is usually very weak; B ind ~ -B app 10 -5 [Exception: Superconductors exhibit perfect diamagnetism  they exclude all magnetic fields] Ferromagnetic (iron, cobalt, nickel,…) Somewhat like paramagnetic, the dipoles prefer to line up with the applied field. But there is a complicated collective effect due to strong interactions between neighboring dipoles  they tend to all line up the same way. Very strong enhancement. B ind ~ B app 10 +5

23. 2/26/2016 22 Even in the absence of an applied B, the dipoles tend to strongly align over small patches – “domains”. Applying an external field, the domains align to produce a large net magnetization. “Soft” ferromagnets The domains re-randomize when the field is removed “Hard” ferromagnets The domains persist even when the field is removed “Permanent” magnets Domains may be aligned in a different direction by applying a new field Domains may be re-randomized by sudden physical shock If the temperature is raised above the “Curie point” (770˚ for iron), the domains will also randomize  paramagnet Magnetic Domains

24. 2/26/2016 23 1A Which kind of material would you use in a video tape? (a) diamagnetic (b) paramagnetic (c) “soft” ferromagnetic 1B How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”?Mini-quiz (d) “hard” ferromagnetic

25. 2/26/2016 24 1A Which kind of material would you use in a video tape? (a) diamagnetic (b) paramagnetic (c) “soft” ferromagnetic Mini-quiz (d) “hard” ferromagnetic Diamagnetism and paramagnetism are far too weak to be used for a video tape. Since we want the information to remain on the tape after recording it, we need a “hard” ferromagnet. These are the key to the information age— cassette tapes, hard drives, ZIP disks, credit card strips,…

26. 2/26/2016 25 1B How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”?Mini-quiz The materials are all “soft” ferromagnets. The external field temporarily aligns the domains so there is a net dipole, which is then attracted to the bar magnet. - The effect vanishes with no applied B field - It does not matter which pole is used. End of paper clip S N

27. IBM introduced the first hard disk in 1957, when data usually was stored on tapes. It consisted of 50 platters, 24 inch diameter, and was twice the size of a refrigerator. 2/26/2016 26 It cost $35,000 annually in leasing fees (IBM would not sell it outright). It’s total storage capacity was 5 MB, a huge number for its time!