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Microwave Engineering
book

Microwave Engineering

by Ahmad Shahid Khan
May 2014
Intermediate to advanced content levelIntermediate to advanced
800 pages
24h 50m
English
CRC Press
Content preview from Microwave Engineering
396 Microwave Engineering
= +
e
m
U B U B U
d
dt
dU
dt
z r r z r
( )
φ
φ
(11.33b)
=
e
m
U B U B
dU
dt
r r
z
( )
φ φ
(11.33c)
As shown in Figure 11.8a, it may be assumed that B = B
0
a
z
and B
r
= B
ϕ
= 0.
Further, an electron (–e) is assumed to enter the eld at t = 0 at r = a,
ϕ
= 0 and
z = 0 with an initial velocity U = U
r0
a
r
. As U
z
= dz/dt = 0 and the particle starts
at z = 0, z remains 0 for all times. Also, U
ϕ
= 0 at t = 0, d
ϕ
/dt =
ω
and U
ϕ
= r
ω
.
Thus, Equation 11.33 may be written as
=
e
m
B r
d r
dt
r
0
2
2
2
ω ω
(11.34a)
e
m
B
dr
dt r
d
dt
r
0
2
1
= ( )ω
(11.34b)
dU
dt
z
= 0
(11.34c)
These equations can be solved by following the procedure used in the case
of the rectangul
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Publisher Resources

ISBN: 9781466591417