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
Woodward effect wikipedia , lookup
Maxwell's equations wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Lorentz force wikipedia , lookup
Time in physics wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Electrical resistance and conductance wikipedia , lookup
Physics1302.300Spring2017 Class18—February27,2017 MainTopics: •Gauss’LawwithDielectrics •Chapter26Summary •Chapter31Circuits Exam2Thursday/Friday Gauss’LawforDielectrics • ConsiderusingGauss’slaw tocalculatetheelectricfield insideadielectricmaterial insertedintoacapacitor. • Thefigureshowsthe relevantgeometry. • Thefluxthroughthe Gaussiansurface(acylinder inthiscase)iszeroexcept throughtherightflat surface: ∫ E ⋅ dA = EA Physics1302.300Spring2017 qfree, enc − qbound, enc ∫ E ⋅ dA = EA = ∈0 2 Gauss’LawforDielectrics • Usingtherelationshipbetweenthefreeandboundcharge yields qfree, enc ∫ E ⋅ dA = ∈0κ • Thisimportantconclusionrelatestheelectricfieldinsidethe dielectrictothefreechargeonthecapacitorandthe dielectricconstant. Physics1302.300Spring2017 3 Chapter 26: Summary Concepts:Capacitors • A capacitor consists of a pair of conducting objects separated by a nonconducting material or vacuum. The objects store electric potential energy once charge has been transferred from one to the other. • A charge-separating device (such as a battery) has some mechanism that moves charge carriers against an electric field. The work done in this process increases the system’s electric potential energy. ©2015PearsonEducation,Inc. Chapter 26: Summary Concepts:Capacitors • A parallel-plate capacitor consists of two parallel conducting plates of surface area A separated by a gap of width d. The electric field is uniform between the plates. • A coaxial capacitor consists of two coaxial conducting cylinders of radii R1 and R2 > R1 and length ℓ >> R2. • A spherical capacitor consists of two concentric conducting spherical shells of radii R1 and R2 > R1. ©2015PearsonEducation,Inc. Chapter 26: Summary QuantitativeTools:Capacitors • The conducting objects in a capacitor carry charges of equal magnitude q but opposite sign. The charge separation produces a potential difference of magnitude Vcap between the objects. The capacitance C of this arrangement is q C≡ . Vcap • Capacitance is measured in farads F, where 1 F ≡ 1 C/V. ©2015PearsonEducation,Inc. Chapter 26: Summary QuantitativeTools:Capacitors • The capacitance of a parallel-plate capacitor is ∈0 A C= . d • The capacitance of a coaxial capacitor is 2π∈0 C= . ln( R2 /R1 ) • The capacitance of a spherical capacitor is R1 R2 C = 4π∈0 . R2 − R1 ©2015PearsonEducation,Inc. Chapter 26: Summary Concepts:Electricfieldenergyandemf • The energy density of an electric field is the energy per unit volume stored in the field. • The emf of any charge-separating device is the work per unit charge done by nonelectrostatic interactions in separating positive and negative charge carriers. ©2015PearsonEducation,Inc. Chapter 26: Summary QuantitativeTools:Electricfieldenergyandemf • The electric potential energy UE stored in a capacitor is 2 q 2 U E = 12 = 12 CVcap = 12 qVcap . C • In air or vacuum, the energy density uE of an electric field is uE = 12 ∈0 E 2 . • The emf of a charge-separating device is Wnonelectrostatic ≡ . q ©2015PearsonEducation,Inc. Chapter 26: Summary Concepts:Dielectrics • A dielectric is a polarizable nonconducting material. A polar dielectric is made up of molecules that have a permanent dipole moment, whereas a nonpolar dielectric consists of molecules that do not have a dipole moment in the absence of an electric field. • A dielectric inserted between the plates of a capacitor becomes polarized by the electric field of the capacitor. This polarization gives the two faces of the dielectric thin layers of charge of equal magnitude but opposite sign. This charge is bound because the charge carriers are not free to move. The charge on the capacitor plates is free because the charge carriers are free to move. ©2015PearsonEducation,Inc. Chapter 26: Summary QuantitativeTools:Dielectrics • The dielectric constant κ of a material between capacitor plates is V0 κ≡ , Vd where V0 is the potential difference across the capacitor without the dielectric and Vd is the potential difference with the dielectric in place. ©2015PearsonEducation,Inc. Chapter 26: Summary QuantitativeTools:Dielectrics • If a capacitor has capacitance C0 without a dielectric, its capacitance with a dielectric is Cd = κC0. • If qfree is the free charge on a capacitor, then the bound charge qbound is κ –1 qbound = qfree . κ • Gauss’s law in matter is qfree, enc ∫ κ E ⋅ dA = ∈0 , where qfree, enc is the free charge enclosed by the Gaussian surface. ©2015PearsonEducation,Inc. Chapter31:ElectricCircuits • Electriccircuitsconsistofcircuitelementsconnectedby conductors. • Inthischapter,wewillfocusontwotypesofcircuits: – DCcircuitsinwhichelectricpotentialsaretime-invariant.Circuit elementsinthesecircuitsareemf sources(batteries)andresistors. – RCcircuitsaretime-dependent.Circuitelementsareemf sources, resistorsandcapacitors. Physics1302.300Spring2017 13 Chapter 31 Preview Looking Ahead: The basic circuit • Circuits that maintain a constant potential difference are known as direct-current circuits or DC circuits. • Circuits are designed to control the flow of charge carriers— the current—in a device. The current then provides energy to the device, allowing it to perform its function. ©2015PearsonEducation,Inc. Chapter 31 Preview Looking Ahead: The basic circuit • An electric circuit is an interconnection of electrical components (circuit elements). • A loop is any closed conducting path through a circuit. • A power source is any device that provides electric potential energy to an electric circuit. ©2015PearsonEducation,Inc. Chapter 31 Preview Looking Ahead: The basic circuit • The potential difference across the terminals of the power source drives charge carriers through the circuit and thereby creates a current in the circuit. • The load in an electric circuit is all the circuit elements connected to the power source. In the load, electric potential energy is converted to other forms of energy. ©2015PearsonEducation,Inc. Chapter 31 Preview Looking Ahead: Current and resistance • A circuit is in steady state when the current has a constant value at all points in the circuit. The current continuity principle states that in steady state, the current is the same at all locations along a single-loop circuit. ©2015PearsonEducation,Inc. Chapter 31 Preview Looking Ahead: Current and resistance • The resistance of a circuit element is a measure of the potential difference across that element for a given current in it. The SI unit of resistance is the ohm Ω, where 1 Ω = 1 V/A. The conductivity σ of a material is a measure of its ability to conduct charge carriers through the material and is measured in SI units of A/(V × m). • When there is a current in a conductor, there must be an electric field in the conductor to cause the current. In a conductor of uniform cross section at steady state, this electric field has the same magnitude everywhere and is parallel to the walls of the conductor. ©2015PearsonEducation,Inc. Chapter 31 Preview Looking Ahead: Circuit loops • A junction (node) is a location in a circuit where more than two wires are connected. • A branch in a circuit is a conducting path between two junctions that is not intercepted by another junction. • According to the branch rule, the current in a branch of a multiloop circuit is the same throughout the branch. ©2015PearsonEducation,Inc. Chapter 31 Preview Looking Ahead: Circuit loops • Two or more circuit elements are connected in series if there is only a single current path through them and the charge carriers flow through one element after the other. • The potential difference across circuit elements connected in series is equal to the sum of the individual potential differences across each circuit element. Two or more circuit elements are connected in parallel if their ends are connected to the same two junctions. The potential differences across circuit elements connected in parallel are always equal. ©2015PearsonEducation,Inc. ElectricCurrent(Chapter31) • Movingchargescompriseanelectriccurrent. • Themediumthroughwhichchargesmoveiscalleda conductor. • Conductorscanbesolids,liquids,gasesorevenvacuum. Movingchargescanbeeitherpositiveornegative. • Conductionbymetalsisprimarilyelectronmotionthrougha fixedpositivelychargedlattice. • Thematerialsmostcommonlyusedasconductorsaremetals, particularlycopperand,insomecases,aluminum.During WorldWarII,themagnetsusedtoseparate235Uforthe HiroshimabombusedsomeofthesilverthebackedtheU.S. dollarasconductors. Physics1302.300Spring2017 21 Calutrons atOakRidge ErnestLawrence Physics1302.300Spring2017 22 FirstWorkingNuclearReactor Physics1302.300Spring2017 23 FirstWorkingNuclearReactor Physics1302.300Spring2017 24 ElectronConductioninMetals • Electronconductioninmetalsisparameterizedbytwo velocities: – Theelectronshavearandomvelocity,whichisprimarilydetermined bytheirtemperature.Highertemperaturesresultinlargerrandom velocities. – Theelectronsalsohaveadriftvelocity,whichissomeorganized motionrelatedtoanelectricfield. – [Metaphor:Imagineacrowdedpartywithdancingonthesideofa hill.Therewillbealotoftoandfromotion,butthecrowdwillalso graduallydriftdownthehillside.] • Theunitsformeasuringcurrentareamperes.Oneampereis oneCoulombpersecondpassingaparticularpoint. Physics1302.300Spring2017 25 MoreonCurrent • Thereareseveralquantitiesrelatedtocurrent. – Current:chargeperunittimepassingapointonaconductor (i, measuredinamperes) – CurrentDensity:currentperunitofconductorcross-sectionalarea (J, measuredinamperespersquaremeter) – DriftVelocity:organizedmotionofchargecarriers(vd,measuredin meterspersecond) – ChargeperChargeCarrier:(q,measuredinCoulombs) – NumberDensityofChargeCarriers:numberofchargecarriersperunit volume(n,measuredinm-3) – Cross-SectionalAreaofConductor(A,measuredinm2) • Thekeyrelationshipsamongthesequantities: J = nqvd i = |J|A Physics1302.300Spring2017 26 ContinuityofCurrent • Thequantityofcurrentinaconductorisconstant. • Iftheconductornarrowsatsomepoint,thecurrentdensity mustincrease.Sincen andq areconstant,thedriftvelocity mustalsoincrease. • Ausefulmetaphorisawaterpipe.Thecross-sectionalareaof awaterpipeiscommonlydecreasedatanozzleinorderto increasethevelocityofthewaterflowand“shoot”thewater further. Physics1302.300Spring2017 27 AmericanWireGauge • IntheUnitedStates,thediameterandcross-sectionalareaof electricalwiresisusuallyspecifiedinaframeworkcalledAWG orAmericanWireGauge.InAWG,thehigherthegauge,the finerthewire.No.36gaugewireis0.005inchesindiameter, No. 0000gaugewireis0.46inchesindiameter. • Householdelectricalcircuitsareusuallyratedateither15or 20amperes.15amperecircuitsgenerallyuse14gaugewire (cross-sectionalarea2.08 mm2).20amperecircuitsgenerally use12gaugewire(area3.31 mm2). Physics1302.300Spring2017 28