浙江师范大学电磁学课件em33.ppt

Sec 3-3 Gauss’s Law in dielectric materials
Given free charge distribution, how to find the steady field and bound charges?
Charge redistribution
E0  E1  E2 · · ·  E
Actual method:Let D involve the effect of bound charges Find D  Find E.
The regular pattern of the field in matter:
Given free charge
 Field
Bound charge
Field redistribution
Iteration method:
··· Condition each other(相互制约)
Gauss’s Law of E :
1. Displacement vector D and Gauss’s Law of D
Substituting
into the above equation yields
Bound charge
Free charge,
Total field,
电介质
自由电荷
S
q0内
q内
Why?
We define the displacement vector as follow:
Gauss’s Law of D :
The flux of the displacement vector through a closed surface equals the algebraic sum of free charges enclosed by the surface.
(1) D lines start from free positive charge and end free negative charge. The flux on the closed surface depends only on the free charge inside the surface.
(2) In general , D is dependent on bound charge. Only when the whole field is filled with matter, D is independent of bound charge.
Explanation:
【Thinking】 From the differential form, how does we understand the fact that D is related to the bound charge distribution ?
2. The relations between D and E, P and E
Differential form of D:
3. Calculation of the field and the bound charge in matter




【Example】 A conducting sphere of radius R with charge q is soaked in an oil. Find the electric field distribution and the bound charge on the oil surface close to the sphere.
R
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
q
q'
R
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
q
q'
From Gauss’s Law of D , we have
P
E
D
r
Why?
Sol.
Method 1:
R
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
q
q'
P
E
D
r
The polarized charge on the oil surface close to the conducting sphere:
-r
^
P(R)
【Thinking】 Is there the volume bound charge in the oil?
q' is always opposite to q in signs.
Method 2:
Using Gauss’s la