Conceptual Physics Electric Potential Circuits Magnetism

Transcription

1 Conceptual Physics Electric Potential Circuits Magnetism Lana Sheridan De Anza College August 3, 2017

2 Last time waves sound electric charge electric field

3 Overview electric potential circuits, current, resistance magnets and magnetic field

4 Warm Up Question Object A has a charge of +2 µc, and object B has a charge of +6 µc. Which statement is true about the electric forces on the objects? (A) F A B = 3F B A (B) F A B = F B A (C) 3F A B = F B A (D) F A B = 3F B A 1 Serway & Jewett, 9th Ed, page 696, Quick Quiz 23.3.

5 Warm Up Question Object A has a charge of +2 µc, and object B has a charge of +6 µc. Which statement is true about the electric forces on the objects? (A) F A B = 3F B A (B) F A B = F B A (C) 3F A B = F B A (D) F A B = 3F B A Newton s 3rd Law! 1 Serway & Jewett, 9th Ed, page 696, Quick Quiz 23.3.

6 Sparking: Electrical Breakdown Electric fields can cause forces on charges. If the field is very strong, it begins to accelerate free electrons which strike atoms, knocking away more electrons forming ions. This starts a cascade, forming a spark.

7 Sparking: Electrical Breakdown Electric fields can cause forces on charges. If the field is very strong, it begins to accelerate free electrons which strike atoms, knocking away more electrons forming ions. This starts a cascade, forming a spark. The strength of the field where this happens is called the critical field, E c, For air E c N/C.

8 Sparking: Electrical Breakdown Electric fields can cause forces on charges. If the field is very strong, it begins to accelerate free electrons which strike atoms, knocking away more electrons forming ions. This starts a cascade, forming a spark. The strength of the field where this happens is called the critical field, E c, For air E c N/C. The air along the spark becomes a plamsa of free charges and can conduct electricity. Sparks look like bright streaks because the air molecules becomes so hot. Accelerating charges radiate, so lightning can also cause radio interference.

9 0 m the curve of Fig a by differentiating with respect to r, ecall Faraday that the Cages derivative of any constant is zero). The curve of e derived A conducting from the shell curves canof shield Fig. the 24-18b interior by integrating from even very withstrong Eq electric fields. E (kv/m) ge spark y and then oss the tire (note ing the perd. (Courtesy ic Fig inside and cal shell o E(r) for t 1 Photo from Halliday, Resnick, Walker

10 Faraday Cages 1 Photo found on TheDailySheeple, credits unknown.

11 Electric Potential Energy A ball on a high shelf has the potential to fall, gaining speed and kinetic energy. The energy the ball stores is gravitational potential energy. Two unlike charges held apart also store electric potential energy U E, since if they are released they will accelerate towards each other.

12 electric potential energy of the charge field system decreases. Energy of a charge in a uniform E-field gravitational potential energy of the object field system decreases. d d q m S E S g a b U E = qed U g = mgd ere the displacement s S points from toward and is par

13 Electric Potential Electric potential is a new quantity that relates the effect of a charge configuration to the potential energy that a test charge would have in that environment. It is denoted V. electric potential, V the potential energy per unit charge: V = U E q V has a unique value at any point in an electric field. It is characteristic only of the electric field, meaning it can be determined just from the electric field.

14 ere the displacement s S points from toward and is par electric potential energy of the charge field system decreases. Potential in a uniform E-field gravitational potential energy of the object field system decreases. d d q m S E S g a V = Ed b (grav. ptl.) = gd

15 Electric Potential Potential is potential energy per unit charge: V = U E q The units are Volts, V. 1 V = 1 J/C = 1 kg m2 A s 3 Volts are also the units of potential difference, the change in potential: V.

16 Electric Potential and Potential Energy Electric potential gives the potential energy that would be associated with test charge q 0 if it were at a certain point P. U E,q0 = q 0 V P 25.3 Electric Potential and Potential Energy Du A potential k e q 1 /r 12 exists at point P due to charge q 1. The potential energy of the pair of charges is given by k e q 1 q 2 /r 12. r12 q 1 r12 q 1 P V 1 k e q 1 r 12 a b q 2 We obtain 1 Figure the from electric Serwaypotential and Jewett, resulting 9th ed. from two or more point charges by

17 Electric Potential A potential and k e q 1 /r 12 Potential The potential Energy energy of exists at point P due to charge q 1. the pair of charges is given by k e q 1 q 2 /r 12. Figure 2 establish V 1 at poi brought r12 q 1 r12 q 1 P V 1 k e q 1 r 12 a The closer two positive or two negative charges are, the higher the potential energy. We obtain the electric potential resulting from two or more point charges by applying the superposition principle. That is, the total electric potential at some point P due to several point charges is the sum of the potentials due to the individual charges. For a group of point charges, we can write the total electric potential at P as The closer a positive charge is to a negative q i charge, the lower the V 5 k e ai (25.12) potential energy. r i Figure 25.8a shows a charge q 1, which sets up an electric field throughout space. The charge also establishes an electric potential at all points, including point P, where the electric potential is V 1. Now imagine that an external agent brings a charge q 2 from infinity to point P. The work that must be done to do this is given by Equation 25.4, W 5 q 2 DV. This work represents a transfer of energy across the boundary of the two-charge system, and the energy appears in the system as potential energy U when the particles are separated by a distance r 12 as in Figure 25.8b. From Equation 8.2, we have W 5 DU. Therefore, the electric potential energy of a By convention, we say that the electric potential V is positive close to a positive charge and negative close to a negative charge. A potential difference, V, will cause free charges to move. b q 2 Elect sever

18 Electric Potential A contour plot of electric potential (dashed lines) around a point charge: tential surface ield line + (b)

19 Electric Field and Electric Potential Potential, V, is potential energy per unit charge: U E = qv Electric field, E, is force per unit charge: F = q E Notice the relation! Both quantities are defined so that we can predict physical quantities associated with putting a charge at a certain point.

20 Circuits Circuits make use of potential differences to create currents. Circuits consist of electrical components connected by wires. Some types of components: batteries, resistors, capacitors, lightbulbs, LEDs, diodes, inductors, transistors, chips, etc.

21 Circuit substitution problem. of is superconducting magne Notice that this the as Equation 26.2 Notice that thisexpression expression is the samesame asthis Equation 26.2, the capa Capacitor section. Th approximately ten times g component symbols symbol initially unchar Use Equation to express the magnetic field in the tromagnets. Such superco In Supercond studying e storing energy. interior of the base solenoid: 26.3circuit Combinations resonance imaging, or MR diagram " Battery 26.3 Combin Find the mutual inductance, noting that magnetic Twothe or more capacitors oftenfo a organs without the need elements. The symbol battery V the equivalent capacitance of c! coil caused flux F BH through the handle s by the magful radiation. orthroughout more capacito Capacitor this Two section. this se wires between symbol initially theuncharged. equivalent capac netic field the base coil is BA: The of direction of the effective flowcapacitor of positive and switches asw In studying electric circuits, this section. Through diagram. Such The a diagra "a number circuit Switch Wireless charging is used ofinitially other cordless ds Battery in ure Open charge is clockwise. capacitor Csymbol 27.6 Electrical elements. Theuncharged. circuit symbolsp symbol! symbol used by some manufacturers of electricwires cars that avoids model for a dire cap In studying electric between the circuit elem I andcircuit switches as wellcircuits, as thesuch colo diagram. In typical electric ing apparatus. Closed is at the higher " Battery Switch ure The symbol for the ca Open elements. The circuit a source such as a battery symbol model for a capacitor, a pair of! switch Figure 26.6 Ssymbol CircuitClosed symbols forisdetermine between the atwires the higher potential and ci is r Let s an express batteries, and switches. Parallel Com and switches as well b capacitors, c symbols Figure 26.6 Circuit for transfer. First, consider thea capacitors, batteries, and Parallel Combination Notice that capacitors areswitches. in Switch uretwo The symbol # Open capacitors to a resistor. (Resistors are Notice that capacitors are in Rin green, Two capacitors as sho!v batteries blue, are and symbol model forconnected a capacitor blue, resistor R batteries are in green, andconnecting " wires also have nation of capacitors. Figure 26. nation of capac switches are in red. The closed switches are in red. The closed Closed is at the higher poten a d whereas capacitors. The left plates of the switch can carry current, some to the resistor. Unles capacitors. The switch can whereas the battery by a conducting wire thecarry open onecurrent, cannot.! Figure 26.6 Circuit symbols for ais capacitor When is conn wires small the open one batteries, cannot. the compared battery bywit a C L capacitors, and switches. Parallel Combinat " inductor L delivered to the wires is ne combination is an LC circu Q max Notice that capacitors are in Two capacitors following acurr pos blue, batteries are in green,then and Imagine closed, both theconne Figure A circuit consistnation of capacitors. switches are in red. The closedcircuit in Figure from late between maximum p ing of a resistor of can resistance R capacitors. The left pl switch carry current, whereas We identify the entire circu S and a battery having a potential cuit is zero, no energy is tr the open one cannot Oscillations the battery by a condu

22 Circuits The different elements can be combined together in various ways to make complete circuits: paths for current to flow from one terminal of a battery or power supply to the other. l Terminal C h h l C + B V + B S Terminal S (a) (b) This 25-4 (a) Battery circuit is B, said switch to S, be and incomplete plates h and while l of capacitor the switch C, is connected open. in a cirb) A schematic diagram with the circuit elements represented by their symbols.

23 s aa ) in time dt,then the current i through that plane is defined as Electric Current i dq (definition of current). (26-1) Electric current, dt I, is the rate of flow of charge through some find defined the charge plane that (cross passes section): through the plane in a time interval om 0 to t by integration: I = q t q dq t i dt, (26-2) q is an amount of charge and t is a time interval. current i may vary with time. he current i nductor has e at planes c. i a a' b b' c 0 The current is the same in any cross section. i c' F e l e s i e t o d l t a c teady-state conditions, the current is the same for planes aa, bb,and

24 Coulombs and Ampères The unit for current is the Ampère, or more commonly, Amp. Using the definition for current, 1 A = 1 C / 1 s. Therefore, we can formally define the unit of charge in terms of the unit of current: 1 C = (1 A)(1 s)

25 negative charges moving horizontally Flow of charge in a circuit ure Rank the current in these four Conventional current is said to flow from the positive terminal to the negative terminal. However, actually it is negatively charged electrons that flow through metal wires: c current, I d + 1 Figure from Serway and Jewett, 9th ed.

26 Electric Current There are two modes for electric current in use: Direct Current (DC) Alternating Current (AC) Direct current flows only in one direction through a wire. A typical source of DC is a battery. Alternating current flows back and forth. It alternates its direction. Household electricity is AC.

27 Current PART 3 Charge will only 26-2 move ELECTRIC when there CURRENT is a net force on it. 683 A supplying a potential difference across two points on a wire will do this. regardless of lectric field can s are available, ting loop is no rial making up them to move electron flow does not vary ucting loop in a hypothetical is defined as i i (a) i i Battery + i (b)

28 Resistance PART 3 When a potential difference 26-2 ELECTRIC is applied CURRENT across a683 conductor, current begins to flow. onducting loop regardless of e potential. No electric field can duction electrons are available, s no current. loop,the conducting loop is no inside the material making up ectrons, causing them to move short time, the electron flow ts steady state (it does not vary r, part of a conducting loop in q passes through a hypothetical rough that plane is defined as current). (26-1) Fig (a) A loop of copper in electrostatic equilibrium.the entire h the plane in a time interval loop is at a single potential, and the electric field is zero at all points inside the copper. (b) Adding a battery t, (26-2) imposes an electric potential difference between the ends of the loop 1 that are connected to the terminals amount of current that will flow? Figure from Halliday, Resnick, Walker, 9th ed. i i i (a) Battery + i (b) However, different amounts of current will flow in different conductors, even when the applied potential difference is the same. What is the characteristic of the conductor which determines the i

29 Resistance Resistance The resistance of a conductor is given by the ratio of the applied potential to the current that flows through the conductor at that potential: R = V I The units of resistance are Ohms, Ω, symbol is the capital Greek letter Omega. 1 Ω = 1 V/A We can think of a high resistance as resisting, or impeding, the flow of current.

30 Ohm s Law Ohm s Law The current through a device is directly proportional to the potential difference applied across the device. Not all devices obey Ohm s Law! In fact, for all materials, if V is large enough, Ohm s law fails. They only obey Ohm s law when the device s resistance is independent of the applied potential difference.

31 V is high V Ohm s Law (fro +? As we just discussed in Section 26-4, a resisto (wit Obeys Ohm s i law: i resistance. Does not It Potential has obey that difference Ohm s same resistance (V) no matter cau law: (a) ( polarity) of the applied (b) potential difference ar ever, might have resistances that change with pas th Figure 26-11a shows how to distinguish is su t +2 V is applied across the device being tested, and dev +4 device is measured as V is varied in both magn diff 0 V is arbitrarily +2 taken to be positive when the dev higher potential than the right terminal. The 0 is m 2 (from left to right) is arbitrarily assigned a pl not (with the 2 right terminal at a higher potential Potential difference (V) causes is assigned Potential a minus difference sign. (V) Ohm (b) Figure 26-11b is (c) a plot of i versus V for one passing through the origin, so the ratio i/v (whi O We can write this linear relationship Fig. is the as26-11 V same = IR for (a) A all ifpotential and values only difference of V. RThis is V means t is applied to the terminals of a device, pr constant device is independent of the magnitude and +4 and independent of V. establishing a current i.(b) A plot of current i versus difference V. applied potential difference V (Th +2 when Figure the device 26-11c is a is 1000 a plot resistor. for another (c) A conducti term However, notice that we can always device define plot when only R(V the when ) device the = V is a polarity I even semiconducting of when V is positive resi an resistance 0 does depend on V. is pnmore junction than diode. about 1.5 V.When current does tion ex not linear; it depends on the value of the applied We distinguish between the two types ofa Potential difference (V) Ohm s Law Current (ma) Current (ma) Curre Current (ma)

32 Exotic Conductors Conductors materials through which charge can move readily Insulators (also called nonconductors) are materials that charge cannot move through freely Semiconductors are materials with behavior between that of conductors and insulators, eg. silicon and germanium Suprerconductors materials that (in the right circumstances) allow charge to flow without any resistance

33 Semiconductors Semiconductors have resistivities between those of conductors and insulators.

34 Semiconductors Semiconductors have resistivities between those of conductors and insulators. However, their resistivities can be controlled by several different means (depending on the type of semiconductor): by adding impurities during manufacture by electric fields by light This allows for many new kinds of components in circuits: ones that amplify currents, emit light, are light sensitive, implement switching, etc.

35 Superconductors Superconducting materials are elements, alloys, or compounds PART that 3 exhibit a remarkable property: below some characteristic 26-9 SUPERCONDUCTORS 697 temperature the resistivity of the material is effectively zero. not only free ire; thus, the electrons so y enough ensulator. Thus, e no current Resistance ( Ω ) Temperature (K) uired to free Fig The resistance of mercury ply electrons Examples ofdrops theseto materials zero a are temperature mercury and of about lead. 4Not K. all rial and materials thus do this! Copper does not. miconductor, a current Mercury and is superconducting below 4 K. ( 269 C)

36 Superconductors Before 1986, it seemed we had a good idea about how this happened and why. 1 Drozdov, et al. (2015). Nature 525 (7567): arxiv:

37 Superconductors Before 1986, it seemed we had a good idea about how this happened and why. Then high temperature superconductors were found. These are ceramics. One is yttrium barium copper oxide (YBCO). The highest critical temperature, T c, at atmospheric pressure found so far is 138 K. We do not really understand why these ceramics are superconductors. Hydrogen sulfide becomes a solid metal at extremely high pressures. It has T c = 203 K at around 150 gigapascals pressure. 1 1 Drozdov, et al. (2015). Nature 525 (7567): arxiv:

38 Superconductors Superconductors must be cooled to their critical temperature, however, they make excellent powerful electromagnets. They are used as electromagents in MRI scanners, mass spectrometers, and particle accelerators. 1 Magnet photo by Mai-Linh Doan, Wikipedia; Frog photo by Lijnis Nelemans/High Field Magnet Laboratory/Radboud University Nijmeg.

39 Magnets Like charges, magnets also interact at a distance. They can either attract or repel. Similarly to charges, they can also effect certain kinds of nearby material by magnetizing it. (cf. polarization)

40 Magnets and electrostatics Magnets have similarities to electric charges but also have an important difference from electric charges. It is possible for a positive or negative electric charge to be found on its own: eg. electrons, protons. Magnetic charges are never found on their own. Magnets have a North pole and a South pole. If you break a magnet in two, new North and South poles form: 1 Figure from Wikipedia.

41 Lack of Magnetic Monopoles Breaking a magnet in two: It is impossible to separate a North pole from a South pole.

42 Lack of Magnetic Monopoles Breaking a magnet in two: It is impossible to separate a North pole from a South pole. It is unclear at this time why magnetic monopoles do not exist, but they have never been conclusively observed. Some (unconfirmed) theories predict them, and they may have existed in the early universe. Other theories attempt to explain why they do not exist. None are yet confirmed. As we understand it, magnets always behave similarly to electric dipoles.

43 The Magnetic Field The magnetic field is written B. The units are: 1 Tesla = 1 Newton (1 Coulomb) (1 m/s) = 1 N A 1 m 1

44 The Magnetic Field The magnetic field is written B. The units are: 1 Tesla = 1 Newton (1 Coulomb) (1 m/s) = 1 N A 1 m 1 The Tesla is abbreviated to T. It is a really big unit: 1 T is already a stronger field than you encounter except in extreme circumstances. A more convenient unit (but not an SI unit) is the Gauss: 1 Gauss = 10 4 Tesla

45 Magnetic shielded Field Lines room T Draw magnetic field lines similarly to E-field line: lines emerge from North pole, enter South pole, denser lines means a stronger field. A bar magnet is a like a magnetic dipole: (a) 1 Figure from Halliday, Resnick, Walker, 9th ed. N S loci a un B :. wha the on t Mag We c Simil any p repre are c F magn

46 Magnetic Field Lines Magnetic fields for a horseshoe magnet and a C-shape magnet: N S N S The field lines ru the north pole to south pole. (a) (b) Fig (a) A horseshoe magnet and (b) a C-shaped magnet. (Only som external field lines are shown.) 1 Figure from Halliday, Resnick, Walker, 9th ed.

47 For Earth, the south pole of the dipole is actually in the north. Compasses and the Earth s Magnetic field Geomagnetic north pole Fig Earth s magnetic field represented as a dipole field. The dipole axis Resnick, MM makes Walker, an 9thangle ed, pgof 1 Figure from Halliday, 870. M R S R N M Geographic north pole B The Magne Earth is a hu approximated dles the cente dipole field, w Because moment : i magnitude o with the rota : and interse coast of Gree magnetic fie Earth in the Northern He pole of Earth The dire monly specifi right) betwee

48 Compasses and the Earth s Magnetic field North poles of magnets point northward, so the magnetic pole that points (roughly) North is a south pole The poles of magnets are perhaps more accurately called: north-seeking pole south-seeking pole but almost always they are just called north and south poles.

49 Why are some objects magnetizable? Microscopic view of ferrous metal: The different red and green regions are magnetic domains. Within each domain are atoms with their outermost electrons aligned (green) or oppositely aligned (red). Electron magnetic effects come from two properties. 1 Figure from Wikipedia, by Ra ike.

50 Electron Spin Angular Momentum 872 CHAPTER 32 MAXWELL S EQUATIONS; Electrons have intrinsic angular momentum. This is also called spin and is the main source of magnetism. For an electron, the spin Substituting Spin is an inherent property is opposite of all the electrons. magnetic It cannot be understood with classical dipole mechanics. moment. B S where the pl to the z axis, The qua Fig The spin, spin magnetic 1 Figure from Halliday, Resnick, Walker, 9th ed. : S : µ s Spin magnet be expressed component o

51 lectrons Electron do not Orbital Angular Momentum can an Electrons electron can be thought of as orbiting the nucleus. (In actual on meaning of fact, this is not such an accurate picture.) ysics. If you have a current around a loop you get a magnetic field. The electron in its orbit is like current in a loop: it creates a llows, magnetic in whichfield (as we shall see later). ius that is much z. However, the which we need ircular path of of the negative t i (of positive itude of the orfrom Eq i e r L orb µ orb A v (32-33)

52 Summary electric field and potential circuits, current, resistance magnetism Homework Prepare a 5-8 minute talk for next week. Tuesday, Aug 8. 3 worksheets (due Monday) Hewitt, Ch 22, onward from page 403. Exercises: 50 & 51; Probs: 7 Ch 23, onward from page 421. Exercises: 5; Problems: 1, 3 Will be set on Monday: Ch 24, onward from page 437. Exercises: 21, 37 Ch 25, onward from page 452. Exercises: 25, 39