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General Physics (PHY 2140) Lecture 11 • Electricity and Magnetism • Direct current circuits • Kirchhoff’s rules • RC circuits • Magnetism • Magnets http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 18-19
Department of Physics and Astronomy announces the Fall 2003 opening of The Physics Resource Center on Monday, September 22 in Room 172 of Physics Research Building. Hours of operation: Mondays, Tuesdays, Wednesdays 11 AM to 6 PM Thursdays and Fridays 11 AM to 3 PM Undergraduate students taking PHY2130-2140 will be able to get assistance in this Center with their homework, labwork and other issues related to their physics course. The Center will be open: Monday, September 22 to Wednesday, December 10, 2003.
Lightning Review • Last lecture: • DC circuits • EMF • Resistors in series • 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.
18.4 Kirchhoff’s rules and DC currents • 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: • The sum of currents entering any junction must equal the sum of the currents leaving that junction (current or junction rule) . • The sum of the potential differences across all the elements around any closed-circuit loop must be zero (voltage or loop rule).
a. Junction rule As a consequence of the Law of the conservation of charge, we have: The sum of the currents entering a node (junction point) equal to the sum of the currents leaving. • Similar to the water flow in a pipe. 11
b. Loop rule As a consequence of the Law of the conservation of energy, we have: • 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). • 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 The sum of the potential differences across all the elements around any closed loop must be zero. • 11
b. Loop rule: illustration Loops can be chosen arbitrarily. For example, the circuit below contains a number of closed paths. Three have been selected for discussion. Suppose that for each element, respective current flows from + to - signs. - + v2 - v5 + Path 1 - - - v1 v4 v6 + + + Path 2 v3 v7 - + + - Path 3 - + + v8 v12 v10 + - - + v11 - - v9 +
b. Loop rule: illustration “b” Using sum of the drops = 0 • - + v2 - v5 + - - - Blue path, starting at “a” - v7 + v10 – v9 + v8 = 0 v1 v4 v6 + + + v3 v7 - + + - “a” • Red path, starting at “b” +v2 – v5 – v6 – v8 + v9 – v11 – v12 + v1 = 0 - + + v8 v12 v10 + - - Yellow path, starting at “b” + v2 – v5 – v6 – v7 + v10 – v11 - v12 + v1 = 0 + v11 - - v9 +
Kirchhoff’s Rules: Single-loop circuits Example: For the circuit below find I, V1, V2, V3, V4 and the power supplied by the 10 volt source. • For convenience, we start at point “a” and sum voltage drops =0 in the direction of the current I. +10 – V1 – 30 – V3 + V4 – 20 + V2 = 0 (1) 2. We note that: V1 = - 20I, V2 = 40I, V3 = - 15I, V4 = 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.
Kirchhoff’s Rules: Single-loop circuits (cont.) Using this value of I in Eq. 2 gives: V1 = - 10 V V3 = - 7.5 V V2 = 20 V V4 = 2.5 V P10(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.
18.5 RC circuits • When switch is closed, current flows because capacitor is charging • As capacitor becomes charged, the current slows because the voltage across the resistor is - Vc and Vc gradually approaches . • Once capacitor is charged the current is zero CE 0.63 CE Charge across capacitor RC is called the time constant
Discharging the capacitor in RC circuit • 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 Q 0.37Q Charge across capacitor
Example : charging the unknown capacitor A series combination of a 12 kW 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.
I C R A series combination of a 12 kW 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 kW 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,
Magnetism • 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 acertain 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.
Bar Magnet • 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?
Electric Field Linesof an Electric Dipole Magnetic Field Lines of a bar magnet
S N S N S N Magnetic Monopoles • 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: Even an individual electron has a magnetic “dipole”! • 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!
Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) Source of Magnetic Fields? • 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.
Magnetic Fields in analogy with Electric Fields 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 Fon a charge movingq at r • (emphasis this chapter is on force law)
Magnetic Materials(a simple look at an advanced topic) • Materials can be classified by how they respond to an applied magnetic field, Bapp. • 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: Bind ~ Bapp•10-5 • Diamagnetic (gold, copper, water,…) • The applied field induces an opposing field; again, this is usually very weak; Bind ~ -Bapp•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.Bind ~ Bapp•10+5
Magnetic Domains Ferromagnets, cont. • 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
1B • How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”? Mini-quiz 1A • Which kind of material would you use in a video tape? (a) diamagnetic (c) “soft”ferromagnetic (d) “hard”ferromagnetic (b) paramagnetic
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,… Mini-quiz 1A • Which kind of material would you use in a video tape? (a) diamagnetic (c) “soft”ferromagnetic (d) “hard”ferromagnetic (b) paramagnetic
1B • How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”? End of paper clip S N 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.
A “bit” of history 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. 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!