C. F. Gauss !% [G - 新潟大学Law-2/ -2$ Q :) > = D dS S = D ndS S = v dv v = Q D dS S Q = v dv v...
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C. F. Gauss ('A4> "!%[G #-.aN3 1RBW9 =<BW=:;P $.)+&_] MJ@7J@CJ@N2WT"!%[GY_ X8\OFN2 FNH X8\VDS\*,S\ IB/X8\ N2WTWNHN36 5IBS\NHLOUN2`W N36KZ[ Q0X8\EE?^ V Q D
Transcript of C. F. Gauss !% [G - 新潟大学Law-2/ -2$ Q :) > = D dS S = D ndS S = v dv v = Q D dS S Q = v dv v...
C. F. Gauss
V Q
D
Michael Faraday (UK)
N =
Q0
m2
0
0
Q
Q Q
= Q Q
?
Q
– Q
– Q
E =
Q4 0 12
= Q
D D =
S
E = Q
4 0 1 2
D = 0 E
Q
D = 0 E
S1
S2
Vector
Displacement r = 1
D = Q4 r 2 = Q
4 1 2
S = n S D
Q V
S
S
v
S = n S D
= D S = D n S = D S cos
= D dS
S= D ndS
S
S n
= 0 = 2
= D S
= 0
n D
Q = v dv
v
S = n S D
Q V
S
v
V
S
= ( r )
S V
v = 0
v 0
v = Q
vC
m 3
= D dS
S= Q = v dv
v
Q
v (r) 0 v (r) = 0
Law
Q
= D dSS
= D ndSS
= v dvv
= Q
D dS
S
Q = v dvv
Q = v dv
v
D dSS
D = 0 E = 0
Q4 0 r2
ar = Q4 r2
ar
r
r
dS = r 2sin d d ar
D dS = Q
4 r 2r2sin d d ar ar = Q
4sin d d
D dS
S
=Q
4sin d d
S
=Q
4sin d
= 0
d= 0
2
dS
= Q
42 2 = Q
Q
r d
r sin d dS
D
dS = r d a r sin d a
a
a
Q
������
D Q E = D0
D
D
dS
dS
Q = D dS
S
= D dSS
+ D dSS //
D dS = 0 D dS = D dS
= D dS1
S1
+ D dS2S2
+ ... + 0 + 0
D D
D
D Q E = D0
l
l
D = l
2
D = l
2a
E = l
2 0
a
�� �� ��
S3
l
dS1
dS2
dS3
S2
S1
��
��
��
S = S1 + S2 + S3
D
D // S1
D S2
D S3
Q = D dS
S
= D dSS1
+ D dSS2
+ D dSS3
l 1 = D dS
S
= D dS1S1
+ 0S2
+ 0S3
l = D 2 1
Q
a
r < a
a < r
Dr = 0 E r = 0
Dr = 0 Er =
Q4 r2
E = 0
E = Er ar =
Q4 0 r 2 ar
r
r
= D dS
S
= Dr 4 r2 = 0r
r
= D dS
S
= Dr 4 r2 = Q
a
a
Q
ab
c
Q
r < aa Q
= D dSS
= Dr 4 r 2 = 0
Qb
a D dS
S= Dr 4 r2 = Q
a < r < b
ab
c
Q
b < r < c
E = 0 D = 0
D dS
S= 0
Dr = 0 E r = 0
Dr = 0 Er =
Q4 r2
E = 0
E = Er ar =
Q4 0 r 2 ar
r = b
r
= D dS
S
= Q
r
rr
ab
Q
c < r D dS
S= Dr 4 r2 = Q
E = Er ar =
Q4 0 r 2 ar
Dr = 0 Er =
Q4 r2
Q Q
-Q+
+ +
+
+ +
+ Q Q
-Q+ +
+
Q -Q+
Michael Faraday
c
cba
Er
r
a a
rr
D dS
S= v dv
v
Dr 4 r2 = 43 a3
v = Q
D dS
S= v dv
v
Dr 4 r2 = 43 r3
v
Dr = 0 E r = v
3r
Dr = 0 Er = v
3a3
r2 =Q
4 r 2
E = Er ar = v
3 0
a3
r2 ar =Q
4 0 r 2 ar E = Er ar = v
3 0
r ar
v
a
Er
v3 0
a
v dvv
= v r 2 sin d d dr= 0= 0
2
0
r
r < a a < r
a
= v 2 2 r2 dr
0
a
= 43 a3
v = Q
a < r r < a
= v 2 2 r 2 dr
0
r
= 43 r3
v
D dS
S= D dv
v
Q = v dv
v
D dv
v= v dv
v
D = v
Theorem
Q
= D dSS
= D ndSS
= v dvv
= Q
D dS
S= D dv
v
Theorem Dn Dn
S
v D
D divergence
D= lim
v 0
1v
D dSS
= Dx
x+
Dy
y+
Dz
z
D > 0 D < 0 D = 0
D D D
D
D = 1 D +
D+
Dz
z
D = 1
r2 rr2Dr + 1
r sin
D sin+ 1
r sinD
divergence
D = lim
v 0
1v
D dSS
=D x
x+
D y
y+
Dz
z
D = v
= a x x+ ay y
+ az z
D = a x x
+ ay y+ az z
D x a x + Dy a y + Dz az
D = v
v
r < a
D = 1r2
ddr
r2Dr
Dr = v
3a3
r2
a < r
Dr = v
3r
a
v
D = 1
r2ddr
r2 v
3r = v
D = 1
r2ddr
r 2 v
3a 3
r 2= 0
r
r
����������
a r < a Dr = v
3r
a < r Dr = v
3a3
r2
D = v
x
z
yx = 1
z = 3
y = 2
A= 2xy a x + x 2 a y + 0 az
A dS
S
= AdvV
A dS
S
=
= 0
y = 0
2
– a x dy dzz = 0
3
+ 2 y a x + a yy = 0
2
ax dy dzz = 0
3
+
x 2 ay
x = 0
1
– a y dx dzz = 0
3
+ 2 x ax + x 2 ayx = 0
1
a y dx dzz = 0
3
= 0 + 2 y
y = 0
2
dy dzz = 0
3
– x 2 dx dzx = 0
1
z = 0
3
+ x 2 dx dzx = 0
1
z = 0
3
A=
Ax
x+
Ay
y+
Az
z=
x2 xy+
yx2 +
z0 = 2 y
Adv
V
= 2 y dx dy dzv
= dx0
1
2 y dy0
2
dz0
3
= 12
= 2 y
y = 0
2
dy dzz = 0
3
= 3 y2
0
2= 12
Ax= 0
y = 0
2
– a x dy dzz = 0
3
+ Ax= 1y = 0
2
a x dy dzz = 0
3
+
Ay= 0
x = 0
1
– a y dx dzz = 0
3
+ Ay= 1x = 0
1
a y dx dzz = 0
3
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