EE 1; Homework 4:
DUE MAY 12
TH
Monday 5 PM
(THERE WILL BE A COLLECTION BOX IN FRONT OF MY OFFICE ENGR. IV RM# 66127D)
1)
An electron beam shaped like a circular cylinder of radius
r
0
carries a charge density given by
0
2
1
v
r
ρ
ρ
⎛⎞
−
⎟
⎜
=
⎟
⎜
⎟
⎜
⎝⎠
+
(C/m
3
)
where
ρ
0
is a positive constant and the beam’s axis is coincident with the zaxis.
(a)
Determine the total charge contained in length
L
of the beam.
(b)
If the electrons are moving in the +z direction with uniform speed
u
, determine the
magnitude and direction of the current crossing the zplane.
2)
A coaxial conductor has radii a = 0.8 mm and b = 3 mm and a polystyrene dielectric for
which
ε
r
= 2.56. If
2
ˆ
Pr
r
=
nC/m
2
in the dielectric, find:
(a)
D and E as functions of r.
(b)
Find Vab and
χ
e.
3)
Dielectric breakdown occurs in a material whenever the magnitude of the field
E
exceeds the
dielectric strength anywhere in that material. In the coaxial capacitor of inner and outer radius of
a
and
b
in centimeter,
(a)
At what value of
r
is 
E

maximum?
(b)
What is the breakdown voltage if
a =
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This note was uploaded on 06/18/2008 for the course EE 1 taught by Professor Joshi during the Spring '08 term at UCLA.
 Spring '08
 Joshi

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