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Prob. 4.
1 2 1 1 2
12 1 2 3 3 9 3
( ) 20(10 )[(3, 2,1) ( 4, 0, 6)] (7, 2, 5)
1.8291 0.5226 1.3065 mN
Q^ Q Q Q Q
x y z
Q Q
r r F r r
a a a
Prob. 4.2 (a)
1 2 3 3 0 0
1 2 3 3/ 2 0 0
1 2 3/ 2 3/ 2 0 0
3/ 2 1 2
[(5, 0, 6) (4, 0, 3)] [(5, 0, 6) (2, 0,1)]
If 0, then
9 1 5 1 0 4 (82) 4 (34)
5 82 5 ( ) 9 34 9
z
Q Q
Q Q
E
Q Q
Q Q
E
4 ( ) nC 34
8.3232 nC
(b)
1 2 3/ 2 3/ 2 0 0
3/ 2 3/ 2 1 2
1
If 0, then
3 0 4 (82) 4 (34)
82 82 3 ( ) 12( ) 34 34
x
q
F
qQ qQ
Q Q nC
Q nC
F E
Prob. 4.
y
y=3x/2, z=4 plane
3
0 2 x
2 3 / 2 2 2
0 0 2 2 2 5 2 2 2
0 0
10 mC 10(4) 4
40 20 20(9 / 4) 9(32) 288 mC 2 0 4 5 0
x
s S x y
x x
Q dS x yzdxdy x ydydx z
y x x x dx x x dx
Prob. 4.
2 v^4 cos^ nC v
Q dv z d d dz
2 1 / 4 (^2) 3 4
0 0 0
4 cos (sin ) 0 2 0 0
z d zdz d
(16)(0.5)(sin / 4) 5.657 nC
Prob. 4.
(a)
1 3 2
0
12 4 nC 3 0
L L
x
Q dl x dx
(b) Method 1:
3
2 2
2
2 2 3/ 2
2
3 2
(0, 0, h) - (x, 0, 0) = (-x, 0, h), | |
Since x<<h, we can ignore the x-component.
L
z z
dl
r
r h x
x x h dx
h x
h x dx Q
h h
E r
r = r
E
E a a
Method 2:
Prob. 4.
(a) From eq. (4.26), 9
9
12 10 678.58^ V/m, z> 18 (12) 2 10 678.58 V/m, z< 2 36
s^ z n n n o z
a E a a a a
(b) Similarly, 9
9
12 10 678.58^ V/m, z> 18 (12) 2 10 678.58 V/m, z< 2 36
s^ z n n n o z
a E a a a a
For z > 4 and z < 0, the fields cancel out. For 0 < z < 4, they add up. Thus
E 2 678.58 a (^) z V/m= 1.357 a z kV/m
Prob. 4.
_
9
9 0
Let ( , ) 2 5; 2
Since point ( 1, 0,1) is below the plane,
151.7 303.5 V/m
x y
x y n
x y n
s x^ y n
x y
f x y x y f
f
f
a a
a a a
a a a
a a E a
a a
x
y
a n
