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Transcript
Physics of Technology PHYS 1800 Lecture 29 Introduction Electricity and Charge Section 0 Lecture 1 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 1 PHYSICS OF TOF ECHNOLOGY - PHYS 1800 PHYSICS TECHNOLOGY ASSIGNMENT SHEET Spring 2009Spring Assignment Sheet 2009 Date Day Lecture Feb 16 M Presidents Day 17 Tu Angular Momentum (Virtual Monday) 18 W Review 19 H Test 2 20 F* Static Fluids, Pressure Feb 23 M Flotation 25 W Fluids in Motion 27 F* Temperature and Heat Mar 2 M First Law of Thermodynamics 4 W Heat flow and Greenhouse Effect 6 F* Climate Change Mar 9-13 M-F Spring Break Mar 16 M Heat Engines 18 W Power and Refrigeration 20 F* Electric Charge Mar 23 M Electric Fields and Electric Potential 25 W Review 26 H Test 3 27 F* Electric Circuits Mar 30 M Magnetic Force Review Apr 1 W Electromagnets 3 F Motors and Generators Apr 6 M Making Waves 8 W Sound Waves 10 F* E-M Waves, Light and Color Apr 13 M Mirrors and Reflections Introduction Section 0 Lecture 1 Slide 2 15 W Refraction and Lenses 17 F* Telescopes and Microscopes Apr 20 M Review 22 W Seeing Atoms 24 F The really BIG & the really small INTRODUCTION TO Modern Physics PHYX 2710 May 1 F Final Exam: 09:30-11:20am Chapter No Class 8 5-8 5-8 9 9 9 10 10 10 No Classes 11 11 12 12 13 9-12 13 14 9-12 14 15 15 16 17 17 17 1-17 18 (not on test) 21 (not on test) Homework Due - 6 7 8 - 9 10 11 No test week 12 Fall 2004 * = Homework Handout *Homework Handout Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 2 Physics of Technology PHYS 1800 Lecture 29 Electric Fields and Potentials Introduction Section 0 Lecture 1 Slide 3 Electrostatic Force INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 3 The Electrostatic Force: Coulomb’s Law • Coulomb measured how the electrostatic force varies with distance and quantity of charge. – Since the electrostatic force is so weak, he had to develop special techniques, involving a torsion balance. – The degree of twist of the wire measures the repulsive force between the two charges. • Determining the amount of charge on the balls was more difficult. Introduction Section 0 Lecture 1 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 4 Historical Perspective on Gravity Cavendish Developed a clever way to measure the weak gravitational force between small masses. Confirmed Newton’s Law of Universal Gravitation (and in essence measured the mass of the Earth in comparison GmM earth Fgravity to the kg mass standard). r2 The effect the 320 kg balls of the 1.5 kg balls was about that of a grain of sand! Introduction Section 0 Lecture 1 Slide 5 That’s 20 parts per billion precision!!! INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Wikeapedia has a nice description of the experiment. Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 5 Coulomb’s Law: Amounts of Charge • Although he could not measure absolute quantities of charge on the balls, Coulomb was able to measure the effects due to different relative amounts of charge. – By bringing two identical metal balls into contact, one charged and the other initially uncharged, Coulomb knew he had equal amounts of charge on both balls. – By repeating the process, he could get a ball with exactly half that charge, or one-fourth, etc. – He could then measure how the strength of the electrostatic force varied when the amount of charge was doubled, quadrupled, etc., in addition to how the force varied with distance Introduction Section 0 Lecture 1 Slide 6 between the balls. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 6 Coulomb’s Law • The electrostatic force between two charged objects is proportional to the quantity of each of the charges and inversely proportional to the square of each distance between the charges. kq1q2 F 2 r Introduction Section 0 Lecture 1 7 inSlide units of coulombs (C) Coulomb' s constant k 9 10 9 N m2 /C 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 7 Two positive charges, one 2 C and the other 7 C, are separated by a distance of 20 cm. What is the magnitude of the electrostatic force that each charge exerts upon the other? a) b) c) d) e) q1 2 C 0.32 N 0.63 N 0.70 N 2.02 N 3.15 N F Introduction Section 0 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 r 20 cm 0.2 m kq1q2 r2 9 10 Lecture 1 q2 7 C Slide 8 9 N m2 /C 2 2 106 C7 106 C 0.2 m 2 0.126 N m2 3.15 N 2 0.04 m Electric Fields and Potential Lecture 29 Slide 8 The Electrostatic and Gravitational Forces • The electrostatic force has the same inverse-square dependence on distance as Newton’s law of gravitation. Gm1m2 Fg r2 kq1q2 and Fe 2 r – If we double the distance between the charges, the force falls to one-fourth of the original. – The gravitational force depends on the masses, and the electrostatic force depends on the charges. – Gravity is always attractive; there is no such thing as negative mass. – Gravity is much weaker than the electrostatic force. – Introduction Physicists are still trying to understand the reasons for the Section 0 Lecture 1 Slide 9 relative strengths of the fundamental forces. – The search for a unified field theory that would explain the relationships between all of the fundamental forces is a major area of research in modern theoretical physics. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 9 Three positive charges are located along a line as shown. What is the magnitude of the force exerted on the 0.02-C charge by the 0.10-C charge? a) b) c) d) e) q1 0.02 C 106 2.25 x N 4.5 x 106 N 9.0 x 106 N 1.8 x 107 N 2.7 x 108 N F q2 0.10 C r2m kq1q2 r2 9 10 9 N m2 /C 2 0.02 C0.10 C 2 m 2 4.5 10 6 N (to the right) Introduction Section 0 Lecture 1 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 10 Three positive charges are located along a line as shown. What is the magnitude of the force exerted on the 0.02-C charge by the 0.04-C charge? a) b) c) d) e) q1 0.02 C 1.8 x 106 N 3.6 x 106 N 7.2 x 106 N 1.44 x 107 N 2.88 x 107 N q2 0.04 C r 1m kq1q2 F 2 r 9 10 9 N m2 /C 2 0.02 C0.04 C 1 m 2 7.2 10 6 N (to the left) Introduction Section 0 Lecture 1 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 11 Three positive charges are located along a line as shown. What is the net force exerted on the 0.02-C charge by the other two charges? a) b) c) d) e) 2.25 x 106 N 4.5 x 106 N 9.0 x 106 N 1.8 x 107 N 2.7 x 108 N F F1 F2 7.2 10 6 N 4.5 10 6 N 2.7 10 6 N (to the left) Introduction Section 0 Lecture 1 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 12 Physics of Technology PHYS 1800 Lecture 29 Electric Fields and Potentials Introduction Section 0 Lecture 1 Slide 13 Electric Fields INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 13 The Electric Field • How do the charges exert forces on each other, when they are not even touching? – The concept of an electric field describes how one charge affects the space around it, which then exerts a force on another charge. – The electric field at a given point in space is the electric force per unit positive charge that would be exerted on a charge if it were placed at that point. F kq E electric electric 22 r̂12 q1 r – It is a vector having the same direction as the force on a positive charge placed at that point. E Introduction Section 0 Lecture 1 Slide 14 – Compare this to the gravitational field INTRODUCTION TO Modern Physics PHYX 2710 E gravity Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Fgravity m1 Gm2 2 rˆ12 g rˆ12 r Lecture 29 Slide 14 Two point charges, 3 C and 2 C, are separated by a distance of 30 cm. A third charge q0 is placed between them as shown. The force exerted by q1 on q0 is 10.8 N, and the force exerted by q2 on q0 is 1.8 N. What is the net electrostatic force acting on q0? a) b) c) d) e) 1.8 N to the left 9 N to the right 10.8 N to the right 12.6 N to the right 12.6 N to the left Introduction Section 0 Lecture 1 F F1 F2 10.8 N 1.8 N 9 N (to the right) Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 15 What is the electric field at the location of the charge q0 due to the other two charges? a) b) c) d) e) f) 2.25 N/C to the left 3.0 N/C to the left 4.5 N/C to the left 2.25 N/C to the right 3.0 N/C to the right 4.5 N/C to the right E F q0 9N 4 10 -6 C 2.25 10 6 N/C (to the right) Introduction Section 0 Lecture 1 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 16 Forces and the Electric Field • We can then use the electric field to find the force on any other charge placed at that point: – If the charge q is negative, the minus sign indicates that the direction of the force on a negative charge is opposite to the direction of the field. – The direction of the electric field is the direction of the force exerted on a positive test charge. – We can talk about the field at a point in space even if there Introduction Section 0at Lecture 1 Slide 17 is no charge that point. – The electric field can exist even in a vacuum. – The field concept can also be used to define a gravitational field or a magnetic field, as well as others. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 17 Electric Field and Field Lines • Although Maxwell was the major contributor to the electric field concept, Faraday also developed the idea of field lines as a means of visualizing both the direction and strength of the field. • The direction of the electric field lines around a positive charge can be found by imagining a positive test charge q0 placed at various points around the source charge. • The field has the same Section 0on Lecture directionIntroduction as the force a positive test charge. 1 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 18 Electric Field and Field Lines • Although Maxwell was the major contributor to the electric field concept, Faraday also developed the idea of field lines as a means of visualizing both the direction and strength of the field. • The electric field lines associated with a positive charge are directed radially outward. Introduction Section 0 Lecture 1 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 19 Electric Field and Field Lines • Although Maxwell was the major contributor to the electric field concept, Faraday also developed the idea of field lines as a means of visualizing both the direction and strength of the field. • A positive test charge is attracted to a negative charge. • The electric field lines associated with a negative charge are directed inward, as0 Lecture Introduction Section indicated by the force on a positive test charge, q0. 1 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 20 Dipole Electric Field and Field Lines • An electric dipole is two charges of equal magnitude but opposite sign, separated by a small distance. – You just add the vectors!!! – Electric field lines originate on positive charges and end on negative charges. • The field lines point away from the positive charge, and in toward the negative charge. • Near each charge, the electric field Introduction Section 0 Lecture 1 approximates the field due to a single point charge of the same sign. Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 21 Two charges, of equal magnitude but opposite sign, lie along a line as shown. What are the directions of the electric field at points A, B, C, and D? a) b) c) d) e) A:left, B:left, C:right, D:right A:left, B:right, C:right, D:right A:left, B:right, C:right, D:left A:right, B:left, C:left, D:right A:right, B:left, C:right, D:right Introduction Section 0 Lecture 1 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 22 Physics of Technology PHYS 1800 Lecture 29 Electric Fields and Potentials Introduction Section 0 Lecture 1 Slide 23 Electrostatic Potential INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 23 Electric Potential • The electrostatic force is a conservative force, which means we can define an electrostatic potential energy. – We can therefore define electric potential or voltage. • Two parallel metal plates containing equal but opposite charges produce a uniform electric field between the plates. Introduction Section 0 • This arrangement is an example of a capacitor, a device to store charge. Lecture 1 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 24 Electric Potential • A positive test charge placed in the uniform electric field will experience an electrostatic force in the direction of the electric field. • An external force F, equal in magnitude to the electrostatic force qE, will move the charge q a distance d in the uniform field. • The external force does work on the charge and increases the potential energy of the charge. • The work done by the external force is qEd, the force times the distance. • This is equal to the increase in potential energy of the charge: Introduction Section 0 Lecture 1 Slide PE = qEd. • This is analogous to what happens when a mass m is lifted against the gravitational force. 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 25 Electric Potential • Electric potential is related to electrostatic potential energy in much the same way as electric field is related to electrostatic force. • The change in electric potential is equal to the change in electrostatic potential energy per unit of positive test charge: PEelectric q 1 J/C 1 V PEelectric qV V PEgravity m g h in units of volts (V) Pgravity gh m 1 J/kg 1 m 2 /s 2 PEgravity m Pgravity m in units of (m 2 /s 2 ) • Electric potential and potential energy are closely related, but they are NOT the same. – If the charge q is negative, its potential energy will decrease Introduction 0 Lecture 1 direction Slide 26 when it is Section moved in the of increasing electric potential. • It is the change in potential energy that is meaningful. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 26 Two plates are oppositely charged so that they have a uniform electric field of 1000 N/C between them, as shown. A particle with a charge of +0.005 C is moved from the bottom (negative) plate to the top plate. What is the change in potential energy of the charge? a) b) c) d) e) 0.15 J 0.3 J 0.5 J 0.8 J 1.5 J PE W Introduction Fd qEdSection 0 Lecture 1 Slide 27 (0.005 C)(1000 N/C)(0.03m) INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 0.15 J Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 27 What is the change in electric potential from the bottom to the top plate? a) b) c) d) e) 0.15 V 0.3 V 5V 30 V 150 V Introduction V Section 0 Lecture 1 Slide 28 PE 0.15 J 30 V q 0.005 C INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 28 Relation between Electric Potential and Electric Field • The potential energy of a positive charge increases when we move it against the field. – For a uniform electric field, there is a simple relationship between the magnitude of the electric field and the change in electric potential: V = Ed. • For non-uniform fields, the relationship is more complicated, but the electric potential always increases most rapidly in the direction opposite to the electric field. Introduction Section 0 Lecture 1 • For a positive point charge, the electric potential increases as we move closer to the charge. Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 29 What is lightning? • Most thunderclouds generate a separation of charge resulting in a net positive charge near the top and a net negative charge near the bottom. • The charge separation produces strong electric fields in the cloud as well as between the cloud and earth. • Since moist earth is a reasonably good conductor, a positive charge is induced on the surface of the earth below the cloud. Introduction Section 0 Lecture 1 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 30 Circuits and Electric Potential and Electric Field Moving a charge in an electric field changes the electric PE and electric potential (the voltage!). Thus moving charge (current) is directly related to change in voltage. V= 30 V Sounds like circuits to me!!! Introduction Section 0 Lecture 1 Slide 31 V= 0 V INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 31 Electric Potential and Electric Field of Lightning • The electric field generated can be several thousand volts per meter; the potential difference between the cloud’s base and the earth can easily be several million volts! • This creates an initial flow of charge (the “leader”) along a path that offers the best conducting properties over the shortest distance. • The leader ionizes some of the atoms in the air along that path. • The following strokes all take place along this same path in rapid succession. • The heating and ionizing produce the lightning we see. • The thunder Introduction (sound Section 0 waves) Lecture 1 isSlide produced at the same time, but takes longer to reach us since sound travels slower than light. 32 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 32 Physics of Technology Next Lab/Demo: Electric Charge Electric Circuits Thursday 1:30-2:45 ESLC 46 Ch 12 and 13 Next Class: Wednesday 10:30-11:20 BUS Slide 33318 room Read Ch 13 Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Electric Fields and Potential Lecture 29 Slide 33