Homework #4, Chapters 5 and 6
1.
Within the region 1
5 cm, 0
0.3
, 0
z
2 cm, current density is
given as
J
= (200 cos
)
a
/(
+ 0.01)A/m
2
.
What total current in the
a
direction
crosses the surface:
(a)
= 0, 1
5 cm, 0
z
2 cm?
(b)
= 0.3
,
1
5
cm, and 0
z
2 cm?
(c) Calculate
J
at
= 2 cm,
= 0.15
,
z
= 1 cm.
2.
A certain current density is given as
J
= [100 cos
/(
r
2
+ 1)]
a
r
A/m
2
.
(a) How
much current flows through the spherical cap,
r
= 3, 0
/6, 0
2
?
(b)
What value would
J
av
have if the same total current were produced by a
uniform
current density
J
av
over the cap?
(c) The same total current flows through the cap,
r
= 10, 0
, 0
2
.
Find
.
3.
A conductor of circular cross section is constructed of steel (
6 x 10
6
/
.m) in
the region 0
1 mm, and copper (
= 5.8 x 10
7
/
.m), 1
1.5 mm.
The
total current carried by the
conductor is 100 A.
Calculate:
(a)
J
Cu
; (b)
J
st
; (c)
E
Cu
;
(d)
E
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 Spring '12
 Barker
 Electric Potential, Electromagnet, Electric charge

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