# 12/2/2018. Monday 12/17. Electric Charge and Electric Field

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1 Electricity Test Monday 1/17 Electric Charge and Electric Field 1

2 In nature, atoms are normally found with equal numbers of protons and electrons, so they are electrically neutral. By adding or removing electrons from matter it will acquire a net electric charge with magnitude equal to e times the number of electrons added or removed, N. q Ne q is the total charge N is the number of electrons e is the electrical charge of one electron The electrical nature of matter is inherent in atomic structure. m p m n kg kg m e kg e C coulombs

3 How many electrons are there in one coulomb of negative charge? q Ne 1C N e x10 19 N(1.6 x10 19 C 19 C) electrons It is possible to transfer electric charge from one object to another. The body that loses electrons has The body that loses electrons has an excess of positive charge, while the body that gains electrons has an excess of negative charge. 3

4 LAW OF CONSERVATION OF ELECTRIC CHARGE During any process, the net electric charge of an isolated system remains constant (is conserved). A person scuffing her feet on a wool rug on a dry day accumulates a net charge of 4 C. How many excess electrons does she get? By how much does her mass increase? me kg e C 4x10 6 C N.6x10 mass (.6x10 N( 1.6x10 14 electrons )(9.11x10 C) 31 kg).4x10 16 kg 4

5 Insulators and Conductors Conductor: Charge flows freely Metals Insulator: Almost no charge flows Most other materials Opposite charges attract each other. Like charges repel 5

6 Metal objects can be charged by conduction. Conduction is the transfer of energy by the movement of particles that are in contact with each other. They can also be charged by induction. Induction charging is a method used to charge an object without actually touching the object to any other charged object. 6

7 Three insulating balls are hung from a wooden rod using thread. The three balls are then individually charged via induction. Subsequently, balls A and B are observed to attract each other, while ball C is repelled by ball B. Which one of the following statements concerning this situation is correct? a) A and B are charged with charges of opposite signs; and C is charged with charge that has the same sign as B. b) A and B are charged with charges of the same sign; and C is electrically neutral. c) A is electrically neutral; and C is charged with charge that has the same sign as B. d) B is electrically neutral; and C is charged with charge that has the same sign as A. e) Choices a and c are both possible configurations. Coulomb s Law The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same. 7

8 Coulomb s Law Coulomb s law: F k q q 1 r This equation gives the magnitude of the force between two point charges. q 1 and q are the charges of the two points Unit of charge: coulomb, C The proportionality constant in Coulomb s law is Suppose that two point charges, one with a charge of C and the other with a charge of C, are separated by a distance of.00 meters. Determine the magnitude of the electrical force of repulsion between them. q1 q F k r C 3.00C F (8.988x10 ) 9 F (8.988x10 )(.75) 9 F 6.74x10 N 8

9 Two balloons are charged with an identical quantity and type of charge: -6.5 nc. They are held apart at a separation distance of 61.7 cm. Determine the magnitude of the electrical force of repulsion between them. F k q q 1 r F (8.988x10 ) F (8.988x10 )(1.03x10 ) 7 F 9.6x10 N 9 9 x C x C A Model of the Hydrogen Atom In the Bohr model of the hydrogen atom, the electron is in orbit about the nuclear proton at a radius of 5.9x10-11 m. Determine the speed of the electron, assuming the orbit to be circular. mv q1 q F c k r r 31 (9.11x10 kg) v (8.988x x 10 m (1.7x10 v 4.77x10 v.x ) v 1 m / s 8.x N m / C F k (1.6 x10 ) (5.9 x q 11 1 r q C) m ) 9

10 Assignment Read pg Do pg. 465 Problems #,4,7,1,13 Electricity Test Monday 1/17 10

11 The Electric Field The electric field is the force on a small charge, divided by the charge: DEFINITION OF ELECRIC FIELD The electric field that exists at a point is the electrostatic force experienced by a small test charge placed at that point divided by the charge itself: Spherical Electric Fields F k q q 1 r F k q E 1 q r SI Units of Electric Field: newton per coulomb (N/C) 11

12 Forces exist only when two or more particles are present. Fields exist even if no force is present. The field of one particle only can be calculated. Example 7 An Electric Field Leads to a Force The charges on the two metal spheres and the ebonite rod create an electric field at the spot indicated. The field has a magnitude of.0 N/C. Determine the force on the charges in (a) and (b) 1

13 The Electric Field (a) F q E N C C N o (b) 8 8 F q E.0 N C4.010 C 4810 N o Example 10 The Electric Field of a Point Charge The isolated point charge of q=+15μc is in a vacuum. The test charge is 0.0m to the right and has a charge q o =+15μC. Determine the electric field at point P. E k q x x r (0.0) 9 6 ( )(15 10 ) E 3.4x10 N / C.04 13

14 The Electric Field Superposition principle for electric fields: The Electric Fields from Separate Charges May Cancel Two positive point charges, q 1 =+16μC and q =+4.0μC are separated in a vacuum by a distance of 3.0m. Find the spot on the line between the charges where the net electric field is zero. 14

15 The Electric Field E k q r k C C d E1 E k 3.0m d 3.0m d.0 d d.0 m Electric field lines or lines of force provide a map of the electric field in the space surrounding electric charges. Electric field lines are always directed away from positive charges and toward negative charges. 15

16 Field Lines Electric dipole: two equal charges, opposite in sign: The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. 16

17 The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. 17

18 Which of the diagrams are incorrect? Mr. Kleckner drew the following electric field lines for a configuration of two charges. What did he do wrong? Explain. 18

19 Consider the electric field lines shown in the diagram below. From the diagram what charges do A and B have? 19

20 Field Lines Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line.. The magnitude of the field is proportional to the density of the lines. 3. Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge. Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant. 0

21 Assignment Read pg Do pg. 466 Problems #3,6,8,31,36 Electricity Test Monday 1/17 1

22 Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative potential energy can be defined Change in electric potential energy is negative of work done by electric force Electrical Potential Electrical potential is the potential energy per unit charge and is the amount of electric potential energy that a unitary point electric charge would have if located at any point in space ΔV = -Ed ΔV: change in electrical potential (Volts) E: Constant electric field strength (N/m or V/m) d: distance moved (m) 1 Volt = 1 J/C

23 Electrical Potential Energy ΔEPE = qδv ΔEPE: change in electrical potential energy (J) q: charge moved (C) ΔV: potential difference (V) Electric Potential kq 1 q EPE r EPE kq V q r (for spherically symmetric charges) 3

24 A positive charge accelerates from a region of higher electric potential toward a region of lower electric potential. A negative charge accelerates from a region of lower potential toward a region of higher potential. Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte. This is a simple electric cell. The Electric Battery 4

25 Within a battery, a chemical reaction occurs that transfers electrons from one terminal to another terminal. The maximum potential difference across the terminals is called the electromotive force (emf). The Electric Battery Several cells connected together make a battery, although now we refer to a single cell as a battery as well. 5

26 The electric current is the amount of charge per unit time that passes through a surface that is perpendicular to the motion of the charges. current charge time or I q t One coulomb per second equals one ampere (A). The unit for current is ampere. Electric Current A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn t look much like the physical circuit! 6

27 Electric Current & Circuits 3 things necessary for electric current to flow at a useable rate through a circuit 1. Source of potential difference (increase) - battery. Closed loop conducting pathway - connecting wires 3. Potential downhill (decrease) - resistor 53 Circuit Symbols DC voltage source Capacitor Resistor Electrical Wire Switch Ground 54 7

28 Conventional current is the hypothetical flow of positive charges that would have the same effect in the circuit as the movement of negative charges that actually does occur. Electrical Resistance impedance or opposition to the flow of electric charge by the conductor current is moving through electrical friction all conductors have resistance electrons contacting atoms in metal 56 8

29 The resistance (R) is defined as the ratio of the voltage V applied across a piece of material to the current I through the material. Real batteries have internal resistance Internal resistance (r) due to current passing through metal reduces the actual terminal voltage that battery operates at (later) 58 9

30 Ohmic In many conductors, the resistance is independent of the voltage; this relationship is called Ohm s law. Materials that do not follow Ohm s law are called non ohmic. Unit of resistance: the ohm, Ω. 1 Ω = 1 V/A. Non ohmic A certain circuit contains a battery and a resistor. An instrument to measure the current in the circuit, an ammeter, is connected in between one of the terminals of the battery and one end of the resistor. The graph shows the current in the circuit as the voltage is increased. Which one of the following statements best describes the resistor in this circuit? a) The resistor does not obey Ohm s law. b) The resistor obeys Ohm s law for voltages between zero and twenty-five volts. c) The resistor obeys Ohm s law for voltages between zero and thirty-five volts. d) The resistor obeys Ohm s law for voltages between zero and forty volts. e) The resistor obeys Ohm s law for voltages between thirty and forty volts. 30

31 OHM S LAW V The ratio (potential/current) is a constant, where I V is the voltage applied across a piece of material and I is the current through the material V R I V IR SI Unit of Resistance: ohm (Ω) SI Unit of Current: amperes (amps) Example The filament in a light bulb is a resistor in the form of a thin piece of wire. The wire becomes hot enough to emit light because of the current in it. The flashlight uses two 1.5-V batteries to provide a current of 0.40 A in the filament. Determine the resistance of the glowing filament. V IR V (1.5 V ) R 7.5 I 0.40A 31

32 Ohm s Law: Resistance and Resistors Some clarifications: Batteries maintain a (nearly) constant potential difference (voltage); the current varies. Resistance is a property of a material or device. Current is not a vector but it does have a direction. Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end. Resistivity The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area: The constant ρ, the resistivity, is characteristic of the material. Different materials have different constants 3

33 R L A Example Longer Extension Cords The instructions for an electric lawn mower suggest that a 0- gauge extension cord can be used for distances up to 35 m, but a thicker 16-gauge cord should be used for longer distances. The cross sectional area of a 0-gauge wire is 5.x10-7 Ω m, while that of a 16-gauge wire is 13x10-7 Ω m. Determine the resistance of (a) 35 m of 0-gauge copper wire and (b) 75 m of 16-gauge copper wire. (a) L R A m35 m m 1. 8 (b) L m75 m R A m

34 Resistivity For any given material, the resistivity increases with temperature: temperature coefficient of resistivity R R 1 T o T o Example A toaster uses a Nichrome heating wire. When the toaster is turned on at 0 o C, the initial current is 1.50A. A few seconds later, the toaster warms up and the current now has a value of 1.30A. The average temperature coefficient of resitivity for Nichrome wire is 4.5x10-4. What is the temperature of the heating wire? V V Ro, R R R 1 T T o V V T T ( T 0) T o T 360 C o 34

35 Assignment Do pg #1,4,7,9,1,15,0 Electricity Test Monday 1/17 35

36 OHM S LAW V The ratio (potential/current) is a constant, where I V is the voltage applied across a piece of material and I is the current through the material V R I V IR SI Unit of Resistance: ohm (Ω) SI Unit of Current: amperes (amps) In many conductors, the resistance is independent of the voltage; this relationship is called Ohm s law. Materials that do not follow Ohm s law are called nonohmic. Unit of resistance: the ohm, Ω. 1 Ω = 1 V/A. 36

37 Electric Power Power, as in kinematics, is the energy transformed by a device per unit time: P IV SI Unit of Power: Watt Electric Power The unit of power is the watt, W. For ohmic devices, we can make the substitutions: This gives multiple expressions to use for Power P IV P I R P V R 37

38 Example The Power and Energy Used in a Flashlight In the flashlight, the current is 0.40A and the voltage is 3.0 V. Find (a) the power delivered to the bulb and (b) the energy dissipated in the bulb in 5.5 minutes of operation. a) P IV (0.40 A)(3.0 V ) 1.W b)5.5 min 330sec Energy Pt (1. W )(330sec) 396 J Electric Power What you pay for on your electric bill is not power, but energy the power consumption multiplied by the time. We have been measuring energy in joules, but the electric company measures it in kilowatthours, kwh. 38

39 Example There are approximately 110 million households that use TVs in the United States. Each TV uses, on average, 75 W of power and is turned on for 6.0 hours a day. If electrical energy costs \$0.1 per kwh, how much money is spent every day in keeping 110 million TVs turned on? One TV - (75 W )(6.0 hr) 450 Whr.45kWh million TVs - (.45 )( ) x kwh kwh kwh x kwh 7 ( )(\$0.1 / ) \$5,940, 000 Example In doing a load of clothes, a clothes dryer uses 16 A of current at 40 V for 45 min. A personal computer, in contrast, uses.7 A of current at 10 V. With the energy used by the clothes dryer, how long (in hours) could you use this computer to surf the Internet? P IV, Energy Pt Energy IVt (16 A)(40 V )(700sec) J (.7 A)(10 V ) t t 3000sec 8.9hours 39

40 Example There are approximately 110 million households that use TVs in the United States. Each TV uses, on average, 75 W of power and is turned on for 6.0 hours a day. If electrical energy costs \$0.1 per kwh, how much money is spent every day in keeping 110 million TVs turned on? One TV - (75 W )(6.0 hr) 450 Whr.45kWh million TVs - (.45 )( ) x kwh kwh kwh x kwh 7 ( )(\$0.1 / ) \$5,940, 000 Power in Household Circuits The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire. To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value. 40

41 Power in Household Circuits Fuses are one-use items if they blow, the fuse is destroyed and must be replaced. Fuses are rated according to the current they can handle. Power in Household Circuits Circuit breakers are switches that will open if the current is too high; they can then be reset. 41

42 Example The circuit shown is designed for a 5-A fuse. Will the fuse blow? P I V 100 W lightbuld, I 0.8 A 10V 1800W heater, I 15.0A 10V 350W stereo, I.9A 10 V 100W dryer, I 10.0A 10V Total, I A Yes the fuse will blow Alternating Current Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC). 4

43 In an AC circuit, the charge flow reverses direction periodically. This is accomplished by alternating the polarity of the voltage at the generator. V Vo sin ft 43

44 In circuits that contain only resistance, the current reverses direction each time the polarity of the generator reverses. I Vo sin R R V o ft I sin ft o peak current I sin ft V Vo sin ft I o P IV I o V o sin ft 44

45 For AC circuits P V I rms rms V I R rms P I V rms rms rms I V o o I o V o Example Electrical Power Sent to a Loudspeaker A stereo receiver applies a peak voltage of 34 V to a speaker. The speaker behaves approximately as if it had a resistance of 8.0 Ω. Determine (a) the rms voltage, (b) the rms current, and (c) the average power for this circuit. V 34 V a) V rms o 4 V b V ) rms Irms R 4 V A c ) P I rmsvrms 3.0 A4 V 7 W 45

46 Assignment Do pg #7,8,30,31,3,37 46

47 Electricity Test Monday 1/17 Chapter 19 DC Circuits 47

48 Circuit Symbols Electric circuit needs battery or generator to produce current these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf: This resistance behaves as though it were in series with the emf. 48

49 Example 1 The Terminal Voltage of a Battery The car battery has an emf of 1.0 V and an internal resistance of Ω. What is the terminal voltage when the current drawn from the battery is (a) 10.0 A and (b) A? (a) V Ir 10.0 A V 1.0 V 0.10 V 11.9V (b) V Ir A V 1.0 V 1.0 V 11.0V Circuit in Series 49

50 Circuit in Parallel Circuits Lab 50

51 Electricity Test Monday 1/17 Kirchhoff s rules Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it. Loop rule: The sum of the changes in potential around a closed loop is zero. 51

52 Circuit in Series A series connection has a single path from the battery, through each circuit element in turn, then back to the battery. Circuit in Series The current through each resistor is the same. The voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage. 5

53 Circuit in Series From this we get the equivalent resistance (that single resistance that gives the same current in the circuit). = A 6.00 Ω resistor and a 3.00 Ω resistor are connected in series with a 1.0 V battery. Assuming the battery contributes no resistance to the circuit, find (a) the current, (b) the power dissipated in each resistor, and (c) the total power delivered to the resistors by the battery. a) R S b) P I P I R R 1.33 A A W c) P 10.6 W 5.31 W 15.9 W 10.6 W V I R R S 1.0 V 1.33 A

54 Circuit in Parallel A parallel connection splits the current; the voltage across each resistor is the same: Circuit in Parallel The total current is the sum of the currents across each resistor: 54

55 This gives the reciprocal of the equivalent resistance: = The drawing shows three different resistors in two different circuits. The battery has a voltage of V = 4.0 V, and the resistors have values R 1 = 50.0Ω, R = 5.0Ω and R 3 = 10.0Ω. a) For the circuit on the left, determine the current through and the voltage across each resistor. b) Repeat for the circuit on the right 55

56 The drawing shows three different resistors in two different circuits. The battery has a voltage of V = 4.0 V, and the resistors have values R 1 = 50.0Ω, R = 5.0Ω and R 3 = 10.0Ω. a) For the circuit on the left, determine the current through and the voltage across each resistor. b) Repeat for the circuit on the right a) R eq V 4 I 0.8 A R 85 V (0.8A)(50) 14.1V V V 1 3 (0.8A)(5) 7.1V (0.8A)(10).8V 1 b) R eq Req V 4V I I I 1 3 4V 0.48A 50 4V 0.96A 5 4V.4A The drawing shows a circuit that contains a battery, two resistors, and a switch. What is the equivalent resistance of the circuit when the switch is (a) open and (b) closed? What is the total power delivered to the resistors when the switch is (c) open and (d) closed? a) R b) R eq Req V 9 c) P 1.5W R 65 V 9 d ) P.09 W R

57 Most receivers allow the user to connect to remote speakers in addition to the main speakers. At the instant represented in the picture, the voltage across the speakers is 6.00 V. Determine (a) the equivalent resistance of the two speakers, (b) the total current supplied by the receiver, (c) the current in each speaker, and (d) the power dissipated in each speaker. R P.67 d 1 a) R b R P V rms ) I rms R P c ) P IrmsVrms P I rms V rms V R V R rms ) Irms I rms rms 6.00 V.5 A V A V 1.50 A A6.00 V 4.50 W 1.50 A6.00 V 9.00 W Find the equivalent resistance of the circuit below. 57

58 Step one Step two 58

59 Step three What is the approximate equivalent resistance of the five resistors shown in the circuit? R

60 Assignment Do pg. 547 #1,6,9,13,17 60

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