Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Insulators and Conductors in Equilibrium
Document related concepts
Transcript
Insulators Conductors Insulators and Conductors in Equilibrium PHYS 272 - David Blasing Thursday June 13th 1 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Insulators Definition: Insulator An insulator is a material with no mobile charges. Every electron is bound to an atom. Applying an electric field does not create a current, but does polarize throughout the whole material. 2 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Bulk Polarization Recall that E~ fields polarize individual atoms like p~ = αE~ 3 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Bulk Polarization Recall that E~ fields polarize individual atoms like p~ = αE~ All atoms/molecules in the insulator polarize Larger net effect due to large number of molecules in the insulator 3 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Bulk Polarization Recall that E~ fields polarize individual atoms like p~ = αE~ All atoms/molecules in the insulator polarize Larger net effect due to large number of molecules in the insulator ~net Polarized molecules align with their local E This diagram shows our convention for drawing ~net , polarized molecules: aligned with the local E ~net | and relative lengths ∝ to the local |E 3 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Bulk Polarization Recall that E~ fields polarize individual atoms like p~ = αE~ All atoms/molecules in the insulator polarize Larger net effect due to large number of molecules in the insulator ~net Polarized molecules align with their local E This diagram shows our convention for drawing ~net , polarized molecules: aligned with the local E ~net | and relative lengths ∝ to the local |E The stronger the electric field the larger the “stretch” of the induced dipole Extent of polarization ∝ degree to which the molecule is “stretched” 3 / 25 Insulators Conductors Definition Bulk Polarization Clicker Questions Low Density Assumption The polarized molecules of an insulator make electric fields that affect neighboring molecules 4 / 25 Insulators Conductors Definition Bulk Polarization Clicker Questions Low Density Assumption The polarized molecules of an insulator make electric fields that affect neighboring molecules Formally, p = α|E~applied + E~dipole | and not simply p = α|E~applied | E~dipole is the electric field at the location of one of the molecules due to all the other induced dipoles in the material 4 / 25 Insulators Conductors Definition Bulk Polarization Clicker Questions Low Density Assumption The polarized molecules of an insulator make electric fields that affect neighboring molecules Formally, p = α|E~applied + E~dipole | and not simply p = α|E~applied | E~dipole is the electric field at the location of one of the molecules due to all the other induced dipoles in the material Low-density approximation: the effect of polarized molecules on each other is typically small compared to the effect of the original applied field Low-density approximation: |E~dipole | |E~applied |, hence p = α|E~applied | 4 / 25 Insulators Conductors Definition Bulk Polarization Clicker Questions Difference Between Charged and Polarized Polarized (has a more positive end and a more negative end) and charged (has a non-zero net charge) Polarized but not charged 5 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Clicker Question 1 6 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Clicker Question 2 7 / 25 Definition Bulk Polarization Clicker Questions Insulators Conductors Clicker Question 3 8 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Conductors Definition: Conductor A conductor is a material with a ”sea” of mobile electrons. Electrons in the ”sea” are not bound to an atom, and you can drive a current by applying an electric field. 9 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Definition of Equilibrium Definition: Equilibrium The state in which all all relevant physical properties are no longer changing with respect to a variable of interest 10 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Definition of Equilibrium Definition: Equilibrium The state in which all all relevant physical properties are no longer changing with respect to a variable of interest Examples: 1 Polarization has stopped forming in an insulator 2 Charges have stopped flowing in an conductor 3 Current has saturated in a circuit to a steady value 10 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Model of a Metal 11 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Model of a Metal 1 Electrons are not completely free, they are eventually bound to the metal as a whole. 11 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Model of a Metal 1 Electrons are not completely free, they are eventually bound to the metal as a whole. 2 We will return to this idea when we discuss the force on a current carrying wire in a magnetic field. 11 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Model of a Metal 1 Electrons are not completely free, they are eventually bound to the metal as a whole. 2 We will return to this idea when we discuss the force on a current carrying wire in a magnetic field. 3 In this model, there is no net interaction between mobile electrons 11 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Metal in Electric Field 12 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Metal in Electric Field 12 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Metal in Electric Field 12 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Electric Field inside Metal 13 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Electric Field inside Metal Electric Field inside Metals in Equilibrium E~net = ~0 inside a conductor in static equilibrium. 14 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Electric Field inside Metal Electric Field inside Metals in Equilibrium E~net = ~0 inside a conductor in static equilibrium. 1 Mobile charges on surface rearrange to achieve E~net = ~0 14 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Electric Field inside Metal Electric Field inside Metals in Equilibrium E~net = ~0 inside a conductor in static equilibrium. 1 Mobile charges on surface rearrange to achieve E~net = ~0 2 Actual arrangement might be very complex. 14 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Electric Field inside Metal Electric Field inside Metals in Equilibrium E~net = ~0 inside a conductor in static equilibrium. 1 Mobile charges on surface rearrange to achieve E~net = ~0 2 Actual arrangement might be very complex. 3 This does not mean that metals do not make electric fields, they do make one that makes E~net = ~0. =⇒ E~metal = −E~applied 14 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Ionic Solutions and E~ fields Can you polarization a conductors? Remember that charged particles in a conductor are free to move large distances Ionic solutions are conductors, but the following argument applies to any conductor (ex. metals) 15 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Ionic Solutions and E~ fields Can you polarization a conductors? Remember that charged particles in a conductor are free to move large distances Ionic solutions are conductors, but the following argument applies to any conductor (ex. metals) Suppose that we apply an electric field to the right 15 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Ionic Solutions and E~ fields Can you polarization a conductors? Remember that charged particles in a conductor are free to move large distances Ionic solutions are conductors, but the following argument applies to any conductor (ex. metals) Suppose that we apply an electric field to the right 15 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Ionic Solutions and E~ fields Can you polarization a conductors? Remember that charged particles in a conductor are free to move large distances Ionic solutions are conductors, but the following argument applies to any conductor (ex. metals) Suppose that we apply an electric field to the right What is E~net in the final state? 15 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Ionic Solutions and E~ fields E~net = 0 in the final state. For conductors that are not driven by a battery in a circuit, this is a rule. 16 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Ionic Solutions and E~ fields E~net = 0 in the final state. For conductors that are not driven by a battery in a circuit, this is a rule. Caused by the superposition of two effects: the effect of the external charges (creating E~applied ) the effect of the polarization charges (creating E~IonicSolution) 16 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Ionic Solutions and E~ fields E~net = 0 in the final state. For conductors that are not driven by a battery in a circuit, this is a rule. Caused by the superposition of two effects: the effect of the external charges (creating E~applied ) the effect of the polarization charges (creating E~IonicSolution) However, E~net is not zero while the ionic solution is in the process of polarizing 16 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model E~ fields are not blocked by matter Note: matter (conductors/insulators) do not “block” external E~ fields. E~ext is still fully present inside/behind/around matter. 17 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model E~ fields are not blocked by matter Note: matter (conductors/insulators) do not “block” external E~ fields. E~ext is still fully present inside/behind/around matter. The matter might make another E~ field, E~matter , that makes E~net = ~0. That does not imply that E~ext is some how blocked by the matter. It might, however, be cancelled as far as E~net is concerned by an equal and oppose E~matter . 17 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Rephrased as an Argument by Contradiction 1 Assume that E~net 6= ~0 in equilibrium 18 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Rephrased as an Argument by Contradiction 1 2 Assume that E~net 6= ~0 in equilibrium E~net will exert a force on and then start moving charged particles around 18 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Rephrased as an Argument by Contradiction 1 2 3 Assume that E~net 6= ~0 in equilibrium E~net will exert a force on and then start moving charged particles around This is not an equilibrium state 18 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Rephrased as an Argument by Contradiction 1 2 Assume that E~net 6= ~0 in equilibrium E~net will exert a force on and then start moving charged particles around 3 This is not an equilibrium state 4 Our assumption that E~net 6= ~0 must be wrong. 18 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Rephrased as an Argument by Contradiction 1 2 Assume that E~net 6= ~0 in equilibrium E~net will exert a force on and then start moving charged particles around 3 This is not an equilibrium state 4 Our assumption that E~net 6= ~0 must be wrong. 5 Conclude that E~net = ~0 18 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Excess Charges on Conductors Excess charges on a piece of metal, or any conductor, are always found on an outer or inner surface. It is our convention that only excess charges are drawn on a surface outside the metal. 19 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Group Problem Use either an argument similar to one used with an ionic solution, or another argument by contradiction to prove that the E~ field on the surface of a conductor must be perpendicular to the surface. 20 / 25 Insulators Conductors Definitions Model of a Metal Reaching Equilibrium Drude Model Summary of Conductors and Insulators General Properties of Conductors and Insulators Summarized in the table below. 21 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model Why must there be another force counteracting the acceleration due to an electric field inside a conductor? 22 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model Why must there be another force counteracting the acceleration due to an electric field inside a conductor? If there was not another force, electrons would accelerate to the speed of light if we applied an electric field. The extra force comes from scattering off the charged lattice ions. 22 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model Definition: Drude Model Electrons scatter off fixed atoms in the lattice of a conductor as they move through it. The Drude model roughly approximates this by adding a drag force in the equation of motion for an electron. This creates a fixed upper limit on the current. 23 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model Definition: Drude Model Electrons scatter off fixed atoms in the lattice of a conductor as they move through it. The Drude model roughly approximates this by adding a drag force in the equation of motion for an electron. This creates a fixed upper limit on the current. This is similar to accounting for air drag which leads to a terminal velocity. 23 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model The actual story is much more complicated. 24 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model The actual story is much more complicated. More precisely, electrons freely accelerate for a while, then hit a lattice ion, then accelerate freely, then hit...and so on. 24 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model The actual story is much more complicated. More precisely, electrons freely accelerate for a while, then hit a lattice ion, then accelerate freely, then hit...and so on. The Drude Model averages the free acceleration with the scattering and says that there is an average, ”drift” velocity that the electrons attain. 24 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model Definition: Drift Velocity, ~vd The average velocity in the Drude model of the electrons in a conductor after an equilibrium current has been established 25 / 25 Definitions Model of a Metal Reaching Equilibrium Drude Model Insulators Conductors Drude Model Definition: Drift Velocity, ~vd The average velocity in the Drude model of the electrons in a conductor after an equilibrium current has been established Definition: Electron Mobility µ The constant of proportionality between the drift velocity and the electric field in the Drude model: ~vd = µE~ 25 / 25
