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