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17
Induced Charge
E Eexternal Eadditional 0
By the action of electrostatic force the redistribution of charges in conductor is called the electrostatic induction.
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.
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
36
ExaБайду номын сангаасple
As shown in figure, two charged spherical conductors of radii R2 and R1 connected by a thin conducting wire, where R2 > R1 . The spheres are so far apart that the electric field of one does not influence the other. Find the relationship between the curvature and the surface charge density.
Q P P
uP uQ
24
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.
Eexternal
Definition: Electrostatic Equilibrium The state without the unidirectional electrons motion in the conductor is called an electrostatic equilibrium state of conductor.
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 ▲ ▲ ▲
+ + +
+ + +
13
E0 0
+ + + + + + + +
14
E0 0
+ + + + + + + + + +
15
E0 0
+ + + + + + + + + +
16
an additional electric field E
+ + + + + + + + + + Induced Charge
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.
39
导体上的电荷分布
Point Discharge The electric field due to a charged conductor is large near convex surfaces of the conductor having small radii of curvature and is small near convex surfaces of the conductor having large radii of curvature.
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
Eexternal
The electrostatic induction doesn’t change the total electric quantity in an isolated conductor.
18
E
Einternal Eexternal Eadditional 0
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
E
22
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.
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.
E0 0
3
E0 0
4
E0 0
5
E0 0
+
6
E0 0
+
+
7
E0 0
+ + +
+ +
8
E0 0
+ +
+
9
E0 0
+ + +
+ +
10
E0 0
+ + +
+ +
11
E0 0
+ + +
+
+ + +
12
E0 0
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
E 0
The electric field just outside the charged conductor is perpendicular to the conductor surface.
21
a Uniform Electric Field without Metallic Ball
R1
Q1
l R1
R2
Q2
R2
37
The spheres are at the same potential U.
Q 1 q V 4 0 R2 4 0 R1
1
R2 Q q R 1
2 R2 1R1
38
When an isolated charged conductor is in electrostatic equilibrium state the charge density on the conductor surface is opposite proportional to curvature radius of the surface .
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:
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.
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.
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.
+
+ + + + + + +
28
Proving Select a gaussian surface surrounding the in-surface of the conductor cavity.
In the conductor, E 0
According to Gauss law, we have
