电磁场与电磁波课件：Lecture 12 Electrostatic Energy.pdf

Example Determine the capacitances
e0
of a two-concentric sphere system.
b
a
1
Solution The charges on the inner sphere O
and the outer one can be expressed as follows: 2
C12
C11
ïìqCVCV111101212=+ C
íï 22
ïqCVCV=+
îï 221212220
if q12==0, q 1, thenVV 12== 210, VV 10 = 20;
For rb > region, the field is spherical symmetry
q2 1
VVV22010＝ ===
44pe00bb pe
Put the results in the equations: b
 a
 1 1
 0  C 11  C 12  0 O 2
 4 0 b
 C
1 12
1  C  0  C
 21 22
 4 0 b
C11
C22
ïì C011 =
We obtain íï
ï C4= pe b
îï 22 0
Assume q12==1, q 0, then
1
VV＝ = , ì 1 ba-
110 ï10=´ +C
4 pe0a ï 12
ï 44pe00aab pe
íï
1 ï ba- 1
VV220＝ = , ï 04=+Cbpe
4 pe0b ï 21 0
îï 44pe00ab pe b
ba-