大学物理课件英文版-导体、电容,Conductors,Capacitors.doc

11. ConductorsA conductor is a material in which the electrons at the outer periphery of an atom have no great affinity for any particular individual atom; they are not bounded to individual atom. The electrons can move freely in the conductors.EeFrr=Ere18.1Conductors in electric field22. The conditions of electrostatic equilibrium of a conductor1Charge separation continues until such time that the total electric field within the conductor is zero. Conductor is a equipotentialbody.2The free charge Qon a conductor does not lie within it but must reside on its surface.VE=r18.1Conductors in electric field3. The magnitude of the electric field at the surface of a conductor1In electrostatics, the electric field vector at the surface of a conductor must be perpendicular to the surface.The surface of the conductor is an equipotentialsurface.2The magnitude of the electric field at any location on the surface of any conductor is equal to to the magnitude of the local surface charge density divided by 0.0=E=path anydrEVrr18.1Conductors in electric field300SSS0Sd d d dd1drightleftletera=+=ESSESESESESEQSESQrrrrrrrrrrSrSr18.1Conductors in electric field4.Point dischargelightning rodErErErEFor differently shaped conductors , or for all shapes of conductors in the presence of other conductors or point charges the surface charge density varies with position on the conductor.18.1Conductors in electric field4rRRQrqEERrQqRQErqERQrqVRrRr=22202000/;4444RrQqFor a conductor of arbitrary shape, the electric field at its surface has the greatest magnitude near those portions with the smallest radius of curvature.18.1Conductors in electric field5. An isolated conductor with cavityIf there are no charges in the cavity, then the all charges on the conductor will reside on the out surface of the conductor. The electric field inside the cavity is zero.00d1dS0in=SSESrr18.1Conductors in electric field5s+Is this situation possible?No, in this case, the conductor is not a equipotentialbody.+0=+EErr6.Electrostatic shield18.1Conductors in electric field+qq+ q+No charge on the conductor cavity+qq+ qQ+A charged conductor cavity18.1Conductors in electric field6+qq+ q+qq+ 18.1Conductors in electric fieldVan De Graaffelectrostatic generator18.1Conductors in electric field7Exercise 1:Qa, Qband Sis known, find the 1,2, 3,and 4.+ 4321aQabSbQ1P2Pconductor)2()1(4321baQSSQSS=+=+Charge conservation)3(02222040302011=PE)4(02222040302012=+=PEThe electrostatic equilibrium18.1Conductors in electric fieldSQQSQQbaba2 23241=+=+ 4321aQabSbQ1P2PconductorThe results areIf babaQQQQ=,0,0=SQa3241 0There are no charges on the outboard surface of the conductors.18.1Conductors in electric field818.2 The dielectric in the electric field1. DielectricThere is no freely mobile electron in dielectric, all the electrons are bounded in individual atoms.2. Dielectric in an electric field1polar dielectricsEprrr=2nonpolardielectricsEqFrr=0Er+-+ErHHHHC+-+-+-+-+-+-+-+-+-+-+-The result is emerge the surface charge on the both sides of the dielectric slab.EEE+=rrr03. The electric field in the dielectric18.2 The dielectric in the electric field9For instance:put a dielectric slab in the two conductor planes with charge +Qand Q, respectively.0EEThe electric field in the dielectric +0ErErErErQ+QWe can prove that000=EE0=is called dielectric constant.is called permittivity of dielectric.18.2 The dielectric in the electric field18.3 Capacitors and Capacitance 1. CapacitorA capacitor is a device of storing the charges and the electric energy.Two conductors, isolated electrically from each other and from their surroundings, form a capacitor.10When the capacitor is charged, the conductors, or plates have equal but opposite charges of magnitude Q.For an isolated , ideal, charged capacitor, the charge separation can last indefinitely18.3 Capacitors and Capacitance 2. CapacitanceThe capacitance of a capacitor is defined to be the ratio of the absolute value of the charge on either conductor to the absolute value of the potential difference between them:VQC=(C/V)farad(F)The capacitance of a capacitor is a measure of its capacity for holding (storing )charge.Note:The value of the ratio is independent of either Q or V.18.3 Capacitors and Capacitance 113. Calculating the capacitance1Calculating the electric field;2Calculating the potential difference;3Assuming the absolute charge is Qon one of the plates;4Using the definition of the capacitance.Example 1:A parallelplate capacitorEAQQSEiiS001d=rrQQ18.3 Capacitors and Capacitance EdrErEVrEVVVd=+0ddd0rrrrdAdAEdQVQC00)/(=QQ18.3 Capacitors and Capacitance 12Example 2:A cylindrical capacitorabLrLQErLEQQSEiiS0002)2(1d=rrr18.3 Capacitors and Capacitance abLQrrLQrEVrEVVVbaln2d2dd000=+rrrrabLabLQQVQCln2ln200=18.3 Capacitors and Capacitance 13Example 3:A spherical capacitor20)(inside041drQEQSESiS=rr)(42120RrRrQE=)11(4d4d2102021RRQrrQrEVRR=+rr122104RRRRVQC=R21R18.3 Capacitors and Capacitance Example 4:an isolated sphereThe second conductor is considered to be at infinity.RrQRQV04=RVQC04=4. Capacitor with a dielectric 00EE=The electric field18.3 Capacitors and Capacitance 140VV=00CVQVQC=dAdACC=00)(ln2)(ln200abLabLCC=122112210044RRRRRRRRCC=18.3 Capacitors and Capacitance If the potential difference between the plates of a capacitor is maintained, the effect of a dielectric is to increase the charge on the plates.18.3 Capacitors and Capacitance 15If the charge on the capacitor plates is maintained, the effect of a dielectric is to reduce the potential difference between the plates.18.3 Capacitors and Capacitance 5. Series and parallel combinations of capacitors1capacitors in parallelVCqVCqVCq332211,=VCqqqqeq=+=321321CCCCeq+=18.3 Capacitors and Capacitance 162capacitors in series332211,CqVCqVCqV=)111(321321CCCqVVVV+=+=321eq1111CCCqVC+=18.3 Capacitors and Capacitance Exercise 1:A parallel-plate capacitor of plate area Ais filled with two dielectrics as in Fig. (a) What is the capacitance of the capacitor? If the two dielectrics are filled as in Fig. (b) What is the capacitance of the capacitor? 18.3 Capacitors and Capacitance 17Solution:The capacitor can be viewed as two capacitors C1and C2in parallel,)2()2/()2/(210201021+=+=+=dAdAdACCC18.3 Capacitors and Capacitance The capacitor can be viewed as two capacitors C1and C2in series,Solution:)(22/2/2/2/21210201020102121+=+=+=dAdAdAdAdACCCCC18.3 Capacitors and Capacitance