西南交通大学：《大学物理》课程教学资源（讲稿，双语）CHAPTER 18 Conductors and Dielectric Electric Fields

UNIVERSITY PHYSICS II CHAPTER 18 1 Electric Fields $18.1 Conductors in electric field 1. Conductors A conductor is a material in which the electrons at the outer periphery of an atom have no great affinity for E any particular individual atom; they are not bounded to individual atom The electrons can move freely in the conductors F=-eE

1 1. Conductors A 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. F eE r r = − E r e §18.1 Conductors in electric field

$18.1 Conductors in electric field 2. The conditions of electrostatic equilibrium of a conductor O Charge separation continues until such time that the total electric field within the conductor is zero Conductor equipotential body E=-VV ② The free charge o on a日 conductor does not lie within it but must reside on its surface 18. 1 Conductors in electric field 3. The magnitude of the electric field at the surtace oi a conductor In electrostatics the electric field vector at the surface of a conductor must be perpendicular to the surface. The surface of the conductor is -Av=E dr an equipotential surface. @The 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 o divided by E=

2 2. The conditions of electrostatic equilibrium of a conductor 1Charge separation continues until such time that the total electric field within the conductor is zero. Conductor is a equipotential body. 2The free charge Q on a conductor does not lie within it but must reside on its surface. E = −∇V r §18.1 Conductors in electric field 3. The magnitude of the electric field at the surface of a conductor 1In electrostatics, the electric field vector at the surface of a conductor must be perpendicular to the surface. The surface of the conductor is an equipotential surface. 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 σ divided by ε 0. 0 ε σ E = ∫ − = ⋅ any path V E dr r r ∆ §18.1 Conductors in electric field

$18.1 Conductors in electric field 5E4= “::0+E+:0=E△S= E $18.1 Conductors in electric field 4. Point discharge--lightning rod For 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 44444++4444 亠E /ryttt tttt ttt E∝o

3 0 0 S S S 0 S d d d d d 1 d letera left right ε σ ε σ ε = ∆ ⋅ = ⋅ + ⋅ + ⋅ = ∆ = ⋅ = ∫ ∫ ∫ ∫ ∫ ∫ ∆ ∆ E S E S E S E S E S E S E S Q S Q r r r r r r r r r r S r ∆ S r ∆ §18.1 Conductors in electric field 4.Point discharge—lightning rod E r E r E r E ∝ σ For 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. §18.1 Conductors in electric field

$18.1 Conductors in electric field For a conductor of arbitrary shape, the electric field at its surface has the greatest magnitude near those portions with the smallest radius of curvature O 4Enr4兀E0R O E r aTer E 47e R E R e R ER O/P=T q $18.1 Conductors in electric field 5. An isolated conductor with cavity If 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 Gaussian inside the cavity is zero Ei.ds=ods=0 0 Gaussian

4 r R Q R q r E E R r Q q R Q E r q E R Q r q V R r r R = = = = = = = 2 2 2 0 2 0 0 0 / / ; 4 4 4 4 πε πε πε πε R r Q q For a conductor of arbitrary shape, the electric field at its surface has the greatest magnitude near those portions with the smallest radius of curvature. §18.1 Conductors in electric field 5. An isolated conductor with cavity If 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. 0 d 0 1 d S 0 in = ⋅ = = ∫ ∫ σ σ ε E S S S r r §18.1 Conductors in electric field

$18.1 Conductors in electric field Is this situation possible? S No, in this case, the conductor is not a equipotential body 6. Electrostatic shield $18.1 Conductors in electric field No charge on the a charged conductor conductor cavity cavity Q+q

5 + s − Is this situation possible? No, in this case, the conductor is not a equipotential body. −− − − + + + + + + + + + + + E + E′ = 0 r r 6.Electrostatic shield §18.1 Conductors in electric field + + + + + + + + + + q − q − − − − − − − q + + + + + + No charge on the conductor cavity + + + + + + + + + + q − q − − − − − − − Q+q + + + + + + + + + + + + A charged conductor cavity §18.1 Conductors in electric field

$18.1 Conductors in electric field $18.1 Conductors in electric field Van De graaff electrostatic generator 6

6 + + + + + + + + + + q − q − − − − − − − q + + + + + + + + + + + + + + + + q − q − − − − − − − §18.1 Conductors in electric field Van De Graaff electrostatic generator §18.1 Conductors in electric field

$18.1 Conductors in electric field Exercise 1: @o, ob and s is conductor wn. find the and G12G3 Charge conservation OS+O2S=2 1 S G3S+o=Q(2) Q Q The electrostatic equilibriu E B1 0(3) 28282828 十 十 P? 0(4) 280280280 280 $18.1 Conductors in electric field The results are ductor 2a + 2b o1 O 2S 2a-2b S 2S PI Q f 2>0,0<0,2=g G1=O4=0 There are no charg on the outboard surface ,=-03==a=σ S of the conductors

7 Exercise 1: Qa, Qb and S is known, find the σ1, σ2, σ3, and σ4. + σ 1 σ 2 σ 3 σ 4 Qa a b S Qb • • P1 P2 conductor (2) (1) 3 4 1 2 b a S S Q S S Q + = + = σ σ σ σ Charge conservation 0 (3) 2 2 2 2 0 4 0 3 0 2 0 1 1 = − − − = ε σ ε σ ε σ ε σ EP 0 (4) 2 2 2 2 0 4 0 3 0 2 0 1 2 = + + − = ε σ ε σ ε σ ε σ EP The electrostatic equilibrium §18.1 Conductors in electric field S Q Q S Q Q a b a b 2 2 2 3 1 4 − = − = + = = σ σ σ σ + σ 1 σ 2 σ 3 σ 4 Qa a b S Qb • • P1 P2 The results are conductor If Qa > Qb < Qa = Qb 0, 0, σ σ σ σ σ = − = = = = S Qa 2 3 1 4 0 There are no charges on the outboard surface of the conductors. §18.1 Conductors in electric field

818.2 The dielectric in the electric field 1. Dielectrie There is no freely mobile electron in dielectric all the electrons are bounded in individual atoms 2. Dielectric in an electric field Polar dielectrics T=PXE $18.2 The dielectric in the electric field @nonpolar dielectrics F=qu E .C H e e 士 3. The electric field in the dielectric The result is emerge the surface charge on the both sides of the dielectric slab E=E+e 8

8 §18.2 The dielectric in the electric field 1. Dielectric There is no freely mobile electron in dielectric, all the electrons are bounded in individual atoms. 2. Dielectric in an electric field 1polar dielectrics p E r r r τ = × 2nonpolar dielectrics F qE r r = • • • • • E0 r + + + + + - - - - - + E′ r H H H C H + - - + - + - + - + - + - + - + - + - + - + - The result is emerge the surface charge on the both sides of the dielectric slab. E = E + E′ r r r 0 3. The electric field in the dielectric §18.2 The dielectric in the electric field

818.2 The dielectric in the electric field For instance: put a dielectric slab in the two conductor o -Q planes with charge +o and-2, respectively The electric field in the dielectric E<E We can prove that E <E EE K is called dielectric constant E=Keo is called permittivity of dielectric. 818.3 Capacitors and Capacitance Capacitor A 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. Electric field lines

9 For instance: put a dielectric slab in the two conductor planes with charge +Q and –Q, respectively. E < E0 The electric field in the dielectric + + + + + + + − − − − − − − + + + + + − − − − − E0 r E′ r E r E′ r + Q − Q We can prove that 0 0 0 ε σ κε σ E = < E = κ 0 ε = ε κ is called dielectric constant. is called permittivity of dielectric. §18.2 The dielectric in the electric field §18.3 Capacitors and Capacitance 1. Capacitor A 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

818.3 Capacitors and Capacitance When the capacitor is charged, the conductors or plates have equal but opposite charges magnitude o For an isolated, ideal, Treminal ig charged capacit e charge separation can last indefinitely 818.3 Capacitors and Capacitance 2. Capacitance The capacitance of a capacitor is defined to be the ratio of the absolute value of the charge on ither conductor to the absolute value of th potential difference between them: (C/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 f either o or v. 10

10 When 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 indefinitely §18.3 Capacitors and Capacitance 2. Capacitance The 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: V Q C = (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