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Chapter 16 Electric Charge and Electric Field 16.1 Static Electricity; Electric Charge and Its Conservation Objects can be charged by rubbing 16.1 Static Electricity; Electric Charge and Its Conservation Charge comes in two types, positive and negative; like charges repel and opposite charges attract 16.1 Static Electricity; Electric Charge and Its Conservation Electric charge is conserved – the arithmetic sum of the total charge cannot change in any interaction. Smallest charge Charge on electron = - e Charge on proton = + e 16.2 Electric Charge in the Atom Atom: Nucleus (small, massive, positive charge) Electron cloud (large, very low density, negative charge) 16.2 Electric Charge in the Atom Atom is electrically neutral. Rubbing charges objects by moving electrons from one to the other. 16.2 Electric Charge in the Atom Polar molecule: neutral overall, but charge not evenly distributed 16.3 Insulators and Conductors Conductor: Insulator: Charge flows freely Almost no charge flows Metals Most other materials Some materials are semiconductors. 16.4 Induced Charge; the Electroscope Metal objects can be charged by conduction: 16.4 Induced Charge; the Electroscope They can also be charged by induction: Ground Ground = Infinite sink Of positive Or negative charge 16.4 Induced Charge; the Electroscope Nonconductors won’t become charged by conduction or induction, but will experience charge separation: 16.4 Induced Charge; the Electroscope The electroscope can be used for detecting charge: 16.4 Induced Charge; the Electroscope The electroscope can be charged either by conduction or by induction. 16.4 Induced Charge; the Electroscope The charged electroscope can then be used to determine the sign of an unknown charge. Recap E&M • Thales of Miletus – 600 BC (static electricity) • Han Christian Orstead – 1820 (current and magnetism) • Michael Faraday (1791-1867) – Experimentalist • James Clerk Maxwell (1831-1879) – Theorist • Newton’s Laws – Mechanics • Maxwell’s Equations – E&M 16.5 Coulomb’s Law Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them. 16.5 Coulomb’s Law The force between two charges: Q1Q 2 F12 k 2 F21 r This equation gives the magnitude of the force. Q (or q) represents the magnitude of the charges and r is the distance between them. 16.5 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. 16.5 Coulomb’s Law Unit of charge: coulomb, C The proportionality constant in Coulomb’s law is then: But let' s use k 9 10 N m /C 9 2 2 Charges produced by rubbing are typically around a microcoulomb: 16.5 Coulomb’s Law Charge on the electron: Electric charge is quantized in units of the electron charge. 16.5 Coulomb’s Law The proportionality constant k can also be written in terms of , the permittivity of free space: (16-2) Force • • • • F α product of two charges F α 1/r2 FG = - G (m1 m2)/r2 FC = ±k (q1 q2)/r2 • FC / FG for two protons ~ 2x1039 Review • 2 kinds of charges (+, -) • Unit = Coulomb (proton, electron = ± 1.6 x 10-19 C = ± e • Like repel, opposites attract • Insulators, Conductors • Charge by rubbing, conduction, induction 16.5 Coulomb’s Law Coulomb’s law strictly applies only to point charges. Superposition: for multiple point charges, the forces on each charge from every other charge can be calculated and then added as vectors. 16.6 Solving Problems Involving Coulomb’s Law and Vectors The net force on a charge is the vector sum of all the forces acting on it. Trig Review • • • • SOHCAHTOA sin θ = opposite/hypotenuse cos θ = adjacent/hypotenuse tan θ = opposite/adjacent FX F Cosθ Vectors in 2-D F y FY F Sinθ or FX F Sin FY F Cos φ θ x Vectors in 2-D Part II • May Define a Vector either as FX and FY (Requires coordinate system) F 1 Y • Or: F and θ where θ tan F X F FY FX Force Problem - Force on Q4? (16-15) Q1 = Q3 = +3mC and Q2 = Q4 = -3mC d = 10 cm Q1 Q4 d Q2 Q3 Force Vectors Q1 F41 F42 Q4 F43 d Q2 Q3 Solving Vectors y F42 F41 θ F42y F42x F41x F43y F43 Θ = 450 and F43x = F41y = 0 x y F42 F41 θ F42y F42x F41x F43y x OR tan 1 F4 y F4 x 225 o y θ Q1 d Q2 Q4 F4 Q3 x 16.7 The Electric Field The electric field is the force on a small charge, divided by the charge: (16-3) Electric Field • Put a small positive test charge (q) in a region • Find the force F on that charge • E = F/q • Direction of E is direction the positive test charge moves. 16.7 The Electric Field For a point charge Q and a test charge q: Qq F k 2 r F E q Q E k 2 r 16.7 The Electric Field • • • • Problem solving in electrostatics: electric forces and electric fields Draw a diagram; show all charges, with signs, and electric fields or forces with directions Calculate forces or Electric Fields using Coulomb’s law Add forces or Electric Fields (using vector components) to get result 16.8 Field Lines The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge. 16.8 Field Lines The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge. The electric field is stronger where the field lines are closer together. Line of Charge 16.8 Field Lines Electric dipole: two equal charges, opposite in sign: 2 Like Charges 16.8 Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant. 16.8 Field Lines Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line. 2. 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. Electric Field Problem 16-34 Q1 = Q2 = Q3 = +2.25 μC and d = 1m Q1 E ? d Q2 Q3 y E3 Q1 E2 E1 d Q2 Q3 x Q E k 2 r y E3 E2 x E1 = 2.74 x 104 N/C OR Q 2 Q 1 E E E k 2 1 2k 2 2 d 4 d 2 2 x 2 y tan 1 Ey Ex 45 o y Q1 E 450 x d Q2 Q3 16.11 Electric Forces in Molecular Biology: DNA Structure and Replication Molecular biology is the study of the structure and functioning of the living cell at the molecular level. The DNA molecule is a double helix: 16.11 Electric Forces in Molecular Biology: DNA Structure and Replication The A-T and G-C nucleotide bases attract each other through electrostatic forces. 16.11 Electric Forces in Molecular Biology: DNA Structure and Replication Replication: DNA is in a “soup” of A, C, G, and T in the cell. During random collisions, A and T will be attracted to each other, as will G and C; other combinations will not. Chapter 17 Electric Potential Work W F// d If ΔPE increases W is If ΔPE decreases W is If F d W is 0 and PE 0 In our case F qE and W qE // d 17.1 Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative – potential energy can be defined 17.1 Electrostatic Potential Energy and Potential Difference Electric potential is defined as potential energy per unit charge: (17-2a) Unit of electric potential: the volt (V). 1 V = I J/C. 17.1 Electrostatic Potential Energy and Potential Difference Only changes in potential can be measured, allowing free assignment of V = 0. (17-2b) 17.1 Electrostatic Potential Energy and Potential Difference Analogy between gravitational and electrical potential energy: 17.2 Relation between Electric Potential and Electric Field Work is charge multiplied by potential: Work is also force multiplied by distance: 17.2 Relation between Electric Potential and Electric Field Solving for the field, (17-4b) If the field is not uniform, it can be calculated at multiple points: 17.3 Equipotential Lines If V 0, PE 0 and W 0 Therefore E d An equipotential is a line or surface over which the potential is constant. Electric field lines are perpendicular to equipotentials. 17.3 Equipotential Lines + - Power Supply Voltmeter 17.5 Electric Potential Due to Point Charges The electric potential due to a point charge can be derived using calculus. (17-5) This assumes V = 0 at r = ∞ V for Point Charges Q Vk r This assumes V = 0 at r = ∞ 17.5 Electric Potential Due to Point Charges Using potentials instead of fields can make solving problems much easier – potential is a scalar quantity, whereas the field is a vector. Post Spring Break Review Vectors Direction – opposites Attract, like repel Q E k 2 r Direction – follow positive charge SCALARS Q Vk r Q1Q 2 PE k Q 2 V1 Q1V2 r ΔKE = -ΔPE 4 Types of problem for Chapter 17 • 1) V at a point • 2) Find Potential Energy • 3) Conservation of Potential and Kinetic Energy • 4) Capacitors 1 - Find V for Point Charges Q1 Q Vk r V=? 3 cm 3 cm 4 cm Q2 r1 r2 r Q1 = Q2 = Q = 6 μC 3 cm 4 cm 2 2 5 cm Q1 Q2 Q Vk k 2k r1 r2 r V 2 9 10 2.16 10 9 Nm2 C2 6 Nm C 6 10 C 2 5 10 m 6 2.16 10 6 J C Note: V = 0 if Q2 = -6 μC 2.16 10 V 6 2 -Potential Energy Q1Q 2 PE k Q 2 V1 Q1V2 r PE Work For a point Charge V = 0 at r = ∞ Potential Energy of a System of Charges 1 2 cm 2 cm 3 2 2 cm Q1 = Q2 = Q3 = 2 μC 1st way - Find all combinations of pairs PE SYS Q1Q 3 Q 2Q3 Q1Q 2 k k k r12 r13 r23 Q1Q 2 3k r 2 10 C 2 10 C 3 9 10 2 2 10 m 5.4 N - m 5.4 J 9 N m2 C 6 6 2nd way – Calculate work to build system 1 3 ∞ to 3; W = Q3V2 + Q3V1 ∞ to 1; W = 0 2 ∞ to 2; W = Q2V1 PESYS Q2 V1 Q3V2 Q3V1 kQ1 kQ 2 kQ1 Q2 Q3 Q3 r r r PE SYS Q1Q 3 Q 2Q3 Q1Q 2 k k k r12 r13 r23 3rd Type Conservation of Energy A (+) B (-) VB VA VA > VB E For + Charge PEA > PEB + - For - Charge PEB > PEA A (+) B (-) VB VA E + VA – VB = 200 V ΔKE = -ΔPE KEB- KEA0 = - (PEB – PEA) KEB = PEA – PEB KEB = q(VA – VB) Proton : q = 1.602 x 10-19 C m = 1.67 x 10-27 Kg KEB = q(VA – VB) = (1.602 x 10-19 C)(200V) = 3.2 x 10-17 J New Energy Unit: The Electron Volt One electron volt (eV) is the energy gained by an electron or proton moving through a potential difference of one volt. In our case ; If ΔV = 200 V KEB = 200 eV If KEB = 3.2 x 10-17 J what is the proton’s speed? KE 1 2 2 mv : 17 2KE 2 3.2 10 J v 27 m 1.67 10 Kg 2 10 m/s 5 17.7 Capacitance A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge, create an Electric Field, and store energy. ΔV E +Q -Q 17.7 Capacitance Parallel-plate capacitor connected to battery. (b) is a circuit diagram. 17.7 Capacitance When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage: (17-7) The quantity C is called the capacitance. Unit of capacitance: the farad (F) 1 F = 1 C/V 17.7 Capacitance The capacitance does not depend on the voltage; it is a function of the geometry and materials of the capacitor. For a parallel-plate capacitor: (17-8) 17.8 Dielectrics A dielectric is an insulator, and is characterized by a dielectric constant K. Capacitance of a parallel-plate capacitor filled with dielectric: (17-9) 17.8 Dielectrics Dielectric strength is the maximum field a dielectric can experience without breaking down. 17.8 Dielectrics The molecules in a dielectric tend to become oriented in a way that reduces the external field. 17.8 Dielectrics This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential. 17.9 Storage of Electric Energy A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor. (17-10) 17.7 Energy ΔV +Q E -Q 17.9 Storage of Electric Energy The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field: (17-11) The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful! 17.9 Storage of Electric Energy Heart defibrillators use electric discharge to “jump-start” the heart, and can save lives. Capacitors one more time Both capacitors get charged fully but keep C1 Connected to battery and disconnect C2 Keep C1 Attached to Battery V is constant Add a dielectric K and what Happens to C, Q, PE, E C Q PE E unchanged so = K0 Remove C2 from the Battery Q is constant Add a dielectric K and what Happens to C, V, PE, E C PE V E 17.10 Cathode Ray Tube: TV and Computer Monitors, Oscilloscope A cathode ray tube contains a wire cathode that, when heated, emits electrons. A voltage source causes the electrons to travel to the anode. 17.10 Cathode Ray Tube: TV and Computer Monitors, Oscilloscope The electrons can be steered using electric or magnetic fields. 17.10 Cathode Ray Tube: TV and Computer Monitors, Oscilloscope Televisions and computer monitors (except for LCD and plasma models) have a large cathode ray tube as their display. Variations in the field steer the electrons on their way to the screen. 17.10 Cathode Ray Tube: TV and Computer Monitors, Oscilloscope An oscilloscope displays en electrical signal on a screen, using it to deflect the beam vertically while it sweeps horizontally. 17.11 The Electrocardiogram (ECG or EKG) The electrocardiogram detects heart defects by measuring changes in potential on the surface of the heart. Summary of Chapter 16 • Two kinds of electric charge – positive and negative • Charge is conserved • Charge on electron: • Conductors: electrons free to move • Insulators: nonconductors Summary of Chapter 16 • Charge is quantized in units of e • Objects can be charged by conduction or induction • Coulomb’s law: • Electric field is force per unit charge: Summary of Chapter 16 • Electric field of a point charge: Q Ek 2 r • Electric field can be represented by electric field lines • Static electric field inside conductor is zero; surface field is perpendicular to surface Summary of Chapter 17 • Electric potential energy: • Electric potential difference: work done to move charge from one point to another • Relationship between potential difference and field: Summary of Chapter 17 • Equipotential: line or surface along which potential is the same • Electric potential of a point charge: • Electric dipole potential: Summary of Chapter 17 • Capacitor: nontouching conductors carrying equal and opposite charge •Capacitance: • Capacitance of a parallel-plate capacitor: Summary of Chapter 17 • A dielectric is an insulator • Dielectric constant gives ratio of total field to external field • Energy density in electric field: