Electromagnetics
HW.3
Group.3
Deadline
23
/
7
/
89
1. A hollow spherical shell carries charge density
ρ
=
k
r
2
in the region
a
≤
r
≤
b
. Find the electric ﬁeld in three regions:
r < a
,
a
≤
r
≤
b
,
r > b
.
2. Electric charge with surface density
σ
=
σ
0
cos
2
φ
lies on the circular disk
ρ <
1 in the
xy
plane. Find the electric ﬁeld density at an arbitrary point on
z
axis.
3. A thin conductor ring of radius
R
which has the uniform line charge of
λ
is located on the
xy
plane centered at the origin.(it’s axis is along the
z
axis).
i)Find the electrical ﬁeld on the axis of the ring at an arbitrary distance
z
above
its center. Call this point
P
1
= (0
,
0
, z
).
ii)Now suppose that the point of observation is moved to a very small distance
δρ
from the axis. Call this point
P
2
. As there is no symmetry anymore, the
ﬁeld doesn’t point to the
z
direction, so it has a radial component too. Find the
radial component of the ﬁeld at
P
2
, in the terms of
z
and
δρ
.(hint:use Gauss’s
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 Fall '10
 Rejaei
 Electromagnet, Electric charge, charge density, uniform charge density, uniform line charge, electric field density

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