Electromagnetics
HW.6
Group.3
Deadline
23
/
8
/
89
1. A uniform line charge of
λ
is placed on an infinite straight wire, a distance
d
above a grounded conducting plane.(the wire is parallel to the
x
axis and the
conducting plane is
xy
plane)
i) find the potential in the region above the plane.
ii) find the charge density
σ
induced on the conducting plane.
2.
The applied force from
⃗
p
1
dipole to
⃗
p
2
dipole can be found from the
following relation:
⃗
F
12
=
1
4
πε
0
[
3(
⃗
p
1
.⃗
r
)
⃗
p
2
+ 3(
⃗
p
2
.⃗
r
)
⃗
p
1
+ 3(
⃗
p
1
. ⃗
p
2
)
⃗
r
r
5

15(
⃗
p
1
.⃗
r
)(
⃗
p
2
.⃗
r
)
⃗
r
r
7
]
which
⃗
r
is the vector from
⃗
p
1
to
⃗
p
2
. Now consider there’s a dipole
⃗
p
=
p
0
sin
θ
ˆ
y
+
p
0
cos
θ
ˆ
z
on the
z
axis, a distance
d
above the grounded conducting plane(
xy
plane). Find the force which is applied from the conducting plane to the dipole.
3.
In this problem we want to find the mutual capacity of two cylinders
centered at
x
=
x
01
and
x
=
x
02
and straighten along
z
axis, with radius
R
1
and
R
2
. So solve the following questions hierarchically:
(a). Consider two line charges(
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 Fall '10
 Rejaei
 Cartesian Coordinate System, Electromagnet, Electric charge, Euclidean geometry

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