Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Maxwell's equations wikipedia , lookup
Time in physics wikipedia , lookup
Lorentz force wikipedia , lookup
Electromagnetism wikipedia , lookup
Negative mass wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Anti-gravity wikipedia , lookup
Potential energy wikipedia , lookup
Chapter 21 Electric Potential Topics: • Electric potential energy • Electric potential • Conservation of energy Sample question: Shown is the electric potential measured on the surface of a patient. This potential is caused by electrical signals originating in the beating heart. Why does the potential have this pattern, and what do these measurements tell us about the heart’s condition? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-1 The Potential Inside a Parallel-Plate Capacitor Uelec Q V= = Ex = x q Î0 A Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 Reading Quiz 3. The electric potential inside a parallel-plate capacitor A. B. C. D. E. is constant. increases linearly from the negative to the positive plate. decreases linearly from the negative to the positive plate. decreases inversely with distance from the negative plate. decreases inversely with the square of the distance from the negative plate. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-10 Answer 3. The electric potential inside a parallel-plate capacitor A. B. C. D. E. is constant. increases linearly from the negative to the positive plate. decreases linearly from the negative to the positive plate. decreases inversely with distance from the negative plate. decreases inversely with the square of the distance from the negative plate. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-11 Dielectrics and Capacitors Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectrics and Capacitors The molecules in a dielectric tend to become oriented in a way that reduces the external field. 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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectric Constant With a dielectric between its plates, the capacitance of a parallel-plate capacitor is increased by a factor of the dielectric constant κ: = ke 0 Dielectric strength is the maximum field a dielectric can experience without breaking down. E0 E'= k Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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! Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors and Capacitance (Key Equations) Capacitance • C = |Q| / |Delta V| • Property of the conductors and the dielectric Special Case - Parallel Plate Capacitor • C = Kappa * Epsilon0*A / d Energy • Pee = 1/2 |Q| |Delta V| • |Delta V| = Ed Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electricity key concepts (Chs. 20 & 21) - Slide 1 General Concepts - These are always true Electric Force and Field Model • Charge Model • E-field • Definition • E-field vectors Fe, s®t E= qt • E-field lines å Þ Fe, s®t = qE Ex = E1x + E2 x + E3x + ××× • Superposition E = (note that for forces and fields, we need to work in vector components) net x Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electricity key concepts (Chs. 20 & 21) - Slide 2 General Concepts - These are always true Energy, Electric Potential Energy, and Electric Potential • Energy Definitions: KE, PEe, Peg, W, Esys, Eth and V • Work-Energy Theorem • Conservation of Energy • Work by Conservative force = -- change of PE • Electric Potential Energy and Electric Potential Energy PEe Ve = qt Þ Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. PEe = qVe Electricity - concepts (Chs 20 & 21) General Concepts - These are always true Electric Force and Field Model • Charge Model • E-field • Definition Fe, s®t E= qt Þ Fe, s®t = qE • E-field vectors • E-field lines • Superposition Exnet = E1x + E2 x + E3x + ××× Energy, Electric Potential Energy, and Electric Potential • Energy Definitions: KE, PEe, Peg, W, Esys, Eth and V • Work-Energy Theorem • Conservation of Energy Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electricity - General key concepts (Chs 20 & 21) Charge Model • Electric forces can be attractive or repulsive • Objects with the same sign of charge repel each other • Objects with the opposite sign of charge attract each other • Neutral objects are polarized by charged objects which creates attractive forces between them • There are two kinds of charges, positive (protons) and negative (electrons). In solids, electrons are charge carriers (protons are 2000 time more massive). • A charged object has a deficit of electrons (+) or a surplus of electrons (-). Neutral objects have equal numbers of + and – charges • Fe gets weaker with distance: Fe α 1/r2 • Fe between charged tapes are > Fe between charged tapes & neutral objects • Rubbing causes some objects to be charged by charge separation • Charge can be transferred by contact, conduction, and induction • Visualization => charge diagrams Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Nature of Electric Field Vectors • Test charge is a small positive charge to sample the E-Field • Charge of test charge is small compared to source charges (source charges are the charges that generate the field) • E-field vectors • E-field is the force per charge E = Fe / q • E-field vectors points away from + charges • E-field vectors point towards - charges • E-field for point charges gets weaker as distance from source point charges increases • For a point charge E = Fe / q = [k Q q / r2] / q = k Q / r2 • Electric Force Fe = qE Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field Lines • E-Field lines start on + charges and end on -- charges • Larger charges will have more field lines going out/coming in • Density of Field lines is a measure of field strength – the higher the density the stronger the field • The E-field vector at a point in space is tangent to the field line at that point. If there is no field line, extrapolate Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Definition of Work Work W = F i Dr = F Dr cos a Where a = angle between the vectors Work- Energy Theorem (only valid when particle model applies) Wnet = DKE Work done by a conservative force (Fg, Fs, & Fe) Also work done by conservative force Wg = -DPEg is path independent Conservation of Energy Equation KEi + å PEi + D Esys = KE f + different types Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. å different types PE f + DEth Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 q1q2 PEe = k r12 Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart) Potential Energy for a uniform infinite plate DPEe = -We = - éë Fe × Dr cos a ùû = - ( q E ) Dr cos a For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or inbetween the two plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential Energy per Charge PEe V= qtest DPEe We DV = =qtest qtest Electric Potential increases as you approach positive source charges and decreases as you approach negative source charges (source charges are the charges generating the electric field) A line where V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and PEe= 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Assembling a square of charges Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Analyzing a square of charges Energy to Assemble Wme = PEE = PEEf - PEEi (PEEi = 0 J) PEEf = q1Vnc@1 + q2V1@2 + q3V12@3 + q4V123@4 V123@4 = V1@4 +V2@4 + V3@4 Energy to move (Move 2q from Corner to Center) Wme = ΔPEE = PEEf - PEEi = q2qV123@center - q2qV123@corner Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Problem 21.51 A -10.0 point charge and a +20.0 point charge are 15.0 apart on the x-axis. Part A. What is the electric potential at the point on the x-axis where the electric field is zero? Do not consider x = + or - infinity. Part B. What is the magnitude of the electric field at the point between the charges on the x-axis where the electric potential is zero? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Problem 21.65 Two 2.2 -diameter disks spaced 1.9 apart form a parallel-plate capacitor. The electric field between the disks is 4.6×105 V/m. Part A. What is the voltage across the capacitor? Part B. How much charge is on each disk Part C. An electron is launched from the negative plate. It strikes the positive plate at a speed of 2.1×107 m/s. What was the electron's speed as it left the negative plate? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Problem 21.69 A proton is fired from far away toward the nucleus of an iron atom. Iron is element number 26, and the diameter of the nucleus is 9.0 fm. (1 fm = 1e-15 m.) Assume the nucleus remains at rest. What initial speed does the proton need to just reach the surface of the nucleus? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Example Problem A parallel-plate capacitor is held at a potential difference of 250 V. A proton is fired toward a small hole in the negative plate with a speed of 3.0 x 105 m/s. What is its speed when it emerges through the hole in the positive plate? (Hint: The electric potential outside of a parallel-plate capacitor is zero). Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-26 Example Problem What is Q2? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-35 A Conductor in Electrostatic Equilibrium Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-27 Reading Quiz 4. The electric field A. B. C. D. is always perpendicular to an equipotential surface. is always tangent to an equipotential surface. always bisects an equipotential surface. makes an angle to an equipotential surface that depends on the amount of charge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-12 Answer 4. The electric field A. B. C. D. is always perpendicular to an equipotential surface. is always tangent to an equipotential surface. always bisects an equipotential surface. makes an angle to an equipotential surface that depends on the amount of charge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13 Graphical Representations of Electric Potential Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13 The Potential Inside a Parallel-Plate Capacitor Uelec Q V= = Ex = x q Î0 A Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 Electric Potential of a Point Charge Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-27 Reading Quiz 3. The electric potential inside a parallel-plate capacitor A. B. C. D. E. is constant. increases linearly from the negative to the positive plate. decreases linearly from the negative to the positive plate. decreases inversely with distance from the negative plate. decreases inversely with the square of the distance from the negative plate. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-10 Answer 3. The electric potential inside a parallel-plate capacitor A. B. C. D. E. is constant. increases linearly from the negative to the positive plate. decreases linearly from the negative to the positive plate. decreases inversely with distance from the negative plate. decreases inversely with the square of the distance from the negative plate. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-11