Chapter 9 Conductors and Dielectrics in Electrostatic Field

§9-3 Dielectrics 电介质 §9-4 Gauss’ Law in Dielectric 有电介质时的高斯 定律 Electric Displacement 电位移 §9-5 Energy in Electric Field 电场的能量 §9-2 Capacitance 电容器 §9-1 Conductors 导体 Elecrostatic Induction 静电感应 Elecrostatic Induction 静电感应

Conductor: § 9-1 Conductors and Electrostatic Induction There are many free electrons in it. can move in the conductor randomly e e e e e e e e

1. The phenomena of the electrostatic induction The charges of an insulated conductor are redistributed because of external E-field.

No external E-field The process of electrostatic induction of a conductor

external E-field is supplied-- the electrons start to move. The process of electrostatic induction of a conductor

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor external induced

The process of electrostatic induction of a conductor 静电平衡状态

(2). Electrostatic equilibrium conditions ： (1). Electrostatic equilibrium state ： There is no any charge moving along a definite direction macroscopically inside the conductor or on the surface of the conductor. 2. Electrostatic equilibrium The distribution of charges does not change with time.

 The E-field equals zero everywhere inside the conductor.  The conductor is an equipotential body.  The conductor surface is an equipotential surface.  The E-field at the surface of the conductor is perpendicular to the surface. E=0 The behavior of E-field The behavior of E-potential

Electrostatic field influences conductor: --electrostatic induction --make the charges in conductor redistribution. Conductor influences electrostatic field : -- make the electrostatic field redistribution. Example

The field is uniform before the metal sphere is put in. E

The field is no longer uniform after the metal sphere is put in E

S--any Gaussian surface inside conductor P--any point inside conductor, S--infinite small ， No excess charge inside conductor. (1). Entire conductor ： 3. The charge distribution on conductor at the electrostatic equilibrium state. Prove ： Use No excess charges inside the conductor. They are found only on the conductor surface.

(2). A conductor with a cavity ： Assume charged Q  No charge in the cavity: Prove: Draw a Gaussian surface S surrounding the cavity tightly. No charge inside and internal surface of the conductor. All the excess charges distribute on the outside surface of conductor.

i.e., --No net charge inside S Question ？ Are there any equal magnitude and opposite sign charges on the internal surface of the conductor ？ Inside the conductor Not at all.

 There are charges q in the cavity ： On the inner surface of the conductor ： --induction charges -q On the external surface of the conductor ： The original charges Q of the conductor + induction charges +q

3.The relation about the charge distribution on the conductor surface and the its radius of curvature. Example: Two conducting spheres of different radii connected by a long conducting wire. They are equipotential.

In a qualitative way, for a conductor of arbitrary shape, the charge density distribution on its surface is inverse proportional with its radius of curvature

4. The relation about the E-field just outside the conductor surface and the charge density on the conductor surface.. p is set up by all charges in the space (on and outside the conductor).

5. Application of electrostatic induction. (1).Tip discharge Lighting rod( 避雷针 ) (2).Electrostatic shielding Electrostatic generator candle Electrostatic generator and electric wind

 A conductor shell can shield the external field

 A conductor shell that is connected with the ground can shield the influence of the fields between inside and outside the conductor.

[Example 1]A neutral conductor sphere with radius R is put on the side of a point charge +q. Assume the distance between the spherical center and the point charge is d. Calculate:  The E-field and potential at point 0 set up by the induced charges on the sphere.  If the sphere is connected with the ground, how much is the net charge on the sphere? The examples about electrostatic induction

 Solution The total field at 0 = the field set up by q + the field set up by ±q Assume the induction charges are±q =0 ！！

the potential at 0 set up by ± q : the potential at 0 set up by q :

 the sphere is connected with ground. Assume net charge q 1 is left on the sphere. the potential U 0 at 0 = U q + U q1

[Example 2] Two large parallel plates with the area S carry charge Q a and Q B respectively. QAQA QBQB Find ： The charge and field distribution. solution Assume the charge surface density areσ 1,σ 2,σ 3 andσ 4 on the four surfaces. σ1σ1 σ2σ2 σ3σ3 σ4σ4

Draw a Gaussian surface ⅠⅡ Ⅲ at point P :

and

ⅠⅡ Ⅲ The field distribution: E1E1 E1E1 E2E2 E2E2 E3E3 E3E3 E4E4 E4E4 E=0 inside the plates outside the plates: direction: point to left  point to right 

ⅠⅡ Ⅲ E Ⅰ = E Ⅲ = 0 discussion  Two plates carry equal magnitude and opposite sign charge the charges distribute on the inner surface only.

ⅠⅡ Ⅲ Charges distribute on the exterior surface only.  Two plates carry equal magnitude and same sign charge

[Example 3] conductor sphere with radius r 1 carries ＋ q and conductor spherical shell with inner and exterior radii r 2 and r 3 carries ＋ Q.  Calculate the E distribution, the potential of sphere and shell U 1 and U 2, potential difference △ U  Connect sphere and shell with a wire, find E, U 1 and U 2, △ U =?.  If the shell is connected with ground, find E, U 1, U 2, △ U =?  If the sphere is connected with ground, find the charge distribution. U 2 =?

solution ：  the field distribution:

sphere potential:

The shell potential: Potential difference:

 Connect sphere and shell with a wire, All charges are on the exterior surface of the shell.

The shell is connected with ground, U 2 ＝ 0 ， no any charge on the exterior surface of the shell.

 The sphere is connected with ground, U 1 =0. Assume sphere charges q ' ， then the inner surface of shell charges - q ' ， its exterior surface charges （ Q ＋ q ' ）

As r 3 r 1 < r 3 r 2,  q ' < 0 The potential of shell: