E
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a Metallic Ball in an External Electric Field
++ + + + ++
E
The charges induced on the surfaces of the ball produce an electric field that opposes the external field, giving a resultant field of zero in the conductor. The external field is nonuniform.
B
U B U A E dl
B A
Conclusion A cavity surrounded by conducting walls is a field-free region as long as no charges are inside the cavity.
30
In this chapter, we don’t care about how the electrostatic equilibrium is obtained, but assume the conductor is already in electrostatic equilibrium state, so as to find the distribution of charges , E and U according to Gauss theorem , circulation theorem and conditions of electrostatic equilibrium.
Metallic Conductor and Dielectric in Electrostatic Field
1
Main Contents
Conditions and Properties of a Conductor in Electrostatic Equilibrium. ▲
Properties of a Dielectric in Electrostatic Equilibrium Gauss’s Law in Dielectric ▲ ▲ ▲
b
ua ub E dl E内 0 ua ub
a
b
Q
(2) Suppose there are two arbitrary points P and Q on the surface of the conductor.
Q uP uQ E dl E cos 900 dl 0
+
+ + + + + + +
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Proving Select a gaussian surface surrounding the in-surface of the conductor cavity.
In the conductor, E 0

According to Gauss law, we have
Eexternal
Definition: Electrostatic Equilibrium The state without the unidirectional electrons motion in the conductor is called an electrostatic equilibrium state of conductor.
q1
+
q1
equal and opposite charges
34
electrostatic shielding
35
Relationship Between
and R

R
the surface charge density the curvature radius of a conductor
Eexternal
The electrostatic induction doesn’t change the total electric quantity in an isolated conductor.
18

E

Einternal Eexternal Eadditional 0
E 0
The electric field just outside the charged conductor is perpendicular to the conductor surface.
21
a Uniform Electric Field without Metallic Ball
P S



E 0
qi E dS 0
E 0
q
0
i
0
26
27
Conductor cavity
There is no charge in the cavity.
+
If the conductor is charged, the electric quantity must distribute on the out surface of the conductor.
Idea:
25
(1) The distribution of charges
If the conductor carries charge, the charge resides entirely on its out surface. Solid Conductor
A random gaussian surface is in the conductor.
17
Induced Charge
E Eexternal Eadditional 0
By the action of electrostatic force the redistribution of charges in conductor is called the electrostatic induction.
23
Proving
When a conductor is in electrostatic equilibrium state, the conductor is a body of equal potential, and its surface is a surface of equal potential. (1) Suppose there are two arbitrary points inside p the conductor a and b. a

qi E dS 0
S
0
q 0
i
29
Question
qi 0
A S
Is it possible that on the in-surface there are equivalent and opposite charges? A body of equal potential.
31
There are charges in the cavity.
q2
q1
+ q1
q1 q2
32
导体上的电荷分布
+ + + + +
+q
+
+
+ ++ + + + ++ +
33
Proving If the conductor is originally charged Q and there is a charge q inside the cavity, then there must be the electric quantity Q+q on the out surface, and –q on the in-surface of the conductor.
Calculation of Capacitor
Energy of Electrostatic Field
Important Contents
2
§1. Effects of Conductor in Electrostatic Field
1. Electrostatic Induction and Electrostatic Equilibrium state When there is not electrostatic field, the motion of free electrons in a metal is random, and the metal is neutrality.
Q P P
uP uQ
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2. The Properties of a Conductor in Electrostatic Equilibrium
In the previous chapter, we find E and U on the condition that the distribution of charges is given.
19
20
The electrostatic equilibrium state ——There is no unidirectional motion of charges and the distribution of charges is unchangeable. The electrostatic equilibrium conditions of conductor inside the conductor: