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Electrostatics 10.1 Properties of Electric Charges Static electricity – not moving Two types of charge positive (+) when electrons are lost negative (-) when electrons are gained Objects can gain charges by rubbing 10.1 Properties of Electric Charges Like charges repel Unlike charges attract Law of Conservation of electric charge – the net amount of electric charge produced in a process is zero 10.1 Properties of Electric Charges Robert Millikan – charge is always a multiple of a fundamental unit Quantized – occurs in discrete bundles The discrete bundle is an electron The charge on a single electron is 1.602 x10 19 C 10.1 Properties of Electric Charges 10.2 Insulators and Conductors Conductors – outer electrons of atoms are free to move through the material Insulator – electrons tightly held, do not move 10.2 Insulators and Conductors Semiconductors – conduct electricity under some circumstances, don’t under other conditions Charges can be transferred by contact Called Charging by Conduction 10.2 Insulators and Conductors Induction – charging without contact Object is brought near a charged object Electrons move Object is grounded An electroscope measures if an object has a charge on it 10.2 Insulators and Conductors 10.3 Coulomb’s Law Electric charges apply forces to each other From experiments Force is proportional to charge Inversely proportional to square of distance q1q2 F k 2 r k 8.988 x10 Nm / C 10.3 Coulomb’s Law 9 2 2 Equation – gives magnitude of force Opposite charges – force directed toward each other Like charges – force directed away from each other Charge is measured in Coulombs 10.3 Coulomb’s Law 1 Coulomb is the amount of charge, that if placed 1 m apart would result in a force of 9x109 N Charges are quantized – that is they come in discrete values e 1.602 x10 19 C The constant k relates to the constant called the permittivity of free space 0 8.85 x10 C / Nm 12 2 10.3 Coulomb’s Law 2 These are forces, so be sure to use vector math, draw free body diagrams For multiple objects, require multiple free body diagram 10.3 Coulomb’s Law 10.4 The Electric Field Electrical forces act over distances Field forces, like gravity Michael Faraday electric field – extends outward from every charge and permeates all of space The field is defined by the force it applies to a test charge placed in the field 10.4 The Electric Field The Electric field would then be F Or E kq E 2 r q q is the test charge We can also say that F Eq Remember that E is independent of the test charge. The electric field is also a vector (free body diagrams are probably a good idea) 10.4 The Electric Field 10.5 Electric Field Lines To visualize electric fields Draw electric field lines Direction of the lines is the direction of force on a positive test charge The density of the lines indicates relative strength of the field Note: the field density increase as you get closer 10.5 Electric Field Lines For multiple charges, keep in mind 1. Field lines indicate the direction of the field The actual field is tangent to the field lines 2. The magnitude of the field is relative to the field line density 3. Fields start at positive and end at negatives Field Lines 10.5 Electric Field Lines If the field is produced by two closely spaced parallel plates The field density is constant So the electric field is constant Electric Diple – two point charges of equal magnitude but oppsite sign 10.5 Electric Field Lines 10.6 Conductors in Electrostatic Equilibrium Electrostatic Equilibrium – when no net motion of charge occurs within a conductor 1. The electric field is zero everywhere inside a conductor 2. Any excess charge is on the surface of a conductor 10.6 Conductors in Electrostatic Equilibrium 3. The electric field just outside a charged conductor is perpendicular to the conductors surface 4. The charge accumulates on areas of greatest curvature 10.6 Conductors in Electrostatic Equilibrium 10.7 Potential Difference and Electric Potential Electricity can be viewed in terms of energy The electrostatic force is conservative because it depends on displacement Now PE W PE Fd PE qEd We can calculate this value for a uniform electric field 10.7 Potential Difference and Electric Potential Positive test charge – increases when moved against the field Negative test charge – increases when moved with the field PE V q Electric Potential (Potential) – electric potential energy per unit charge 10.7 Potential Difference and Electric Potential Only difference in potential are meaningful Potential Difference (Electric Potential Difference) – is measureable PE PE V qq Measured in volts (after Alessandro Volta) 1J 1V 1C 10.7 Potential Difference and Electric Potential If we want a specific potential value at a point, we must pick a zero point. That point is usually either A. The ground B. At an infinite distance r 10.7 Potential Difference and Electric Potential 10.8 Electric Potential & Potential Energy Using calculus it can be shown that the electric potential a distance r from a single point charge q is q V k r Assuming that potential is zero at infinity Like Potential Difference, this value is a scalar So 10.8 Electric Potential & Potential Energy 10.9 Potentials and Charged Conductors 1. All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential. 2. The electric potential is a constant everywhere on the surface of a charged conductor in equilibrium. 3. The electric potential is constant everywhere inside a conductor and equal to its value at the surface. 10.9 Potentials and Charged Conductors 10.10 Capacitance Capacitor – device that stores electric charge In RAM, Camera Flash, 10.10 Capacitance Simple capacitors consist of two plate The symbol for a capacitor is The symbol for a cell is The symbol for a battery is 10.10 Capacitance When a potential difference is placed across a capacitor it becomes charged Charging a Capacitor This process takes a short amount of time Time for RC Circuit The charge on each plate is the same, but opposite charge The amount of charge is proportional to the potential difference A constant C (Capacitance) gives Q CV V 10.10 Capacitance Capacitance – Unit Farad 1C 1F 1V For a parallel plate capacitor, the capacitance depends on the area of the plates, the distance between the plates A C o d 10.10 Capacitance Q CV 10.11 Combinations of Capacitors Parallel – more than one pathway For a parallel set of capacitors – the total charge is the sum of the individual charges QT Q1 Q2 ..Qn In all parallel circuits – the potential across each branch is the same as the total VT V1 V2 ..Vn 10.11 Combinations of Capacitors The equivalent capacitance is the value of one capacitor that could replace all those in the circuit with no change in charge or potential Since Q Q Q ..Q T And We combine and get 1 2 Q CV CeqVC C1C V1 C2V2 ..C..nCnVn T eq 10.11 Combinations of Capacitors n Series – components of a circuit are in one pathway The magnitude of the charges is the same on each plate Q Q Q ..Q T 1 2 n 10.11 Combinations of Capacitors The total potential is the sum of the potential drops across each capacitor VT V1 V2 ..Vn We then use that equation and the equation for capacitance Q V We get C Q Q1T Q 11 Q 12 1n .. Ceq C1 C22 Cnn 10.11 Combinations of Capacitors 10.12 Energy Stored in a Charged Capacitor Capacitors store energy Energy can be defined as change in work W QV Or the are under a plot of Q vs. V UW QQVV 11 22 U CV 1 2 2 2 Q U 2C 10.12 Energy Stored in a Charged Capacitor 10.13 Capacitors with Dielectrics Most capacitors have an insulator between the plates Called a Dielectric Increases the capacitance by a factor K Called the dielectric constant o A C K d 10.13 Capacitors with Dielectrics Some Dielectric Constants Material K Paper 3.7 Glass 5 Rubber 6.7 Mica 7 Strontium Titanate 300 10.13 Capacitors with Dielectrics