
731
Appendix A4: Solution to Equations
11.29 and 11.30
Equations 11.28 and 11.29 are reproduced and renumbered as below:
−
− =
e
m
U B U B
dU
dt
y z z y
x
( )
(A4.1a)
−
− =
e
m
U B U B
dU
dt
z x x z
y
( )
(A4.1b)
−
− =
e
m
U B U B
dU
dt
x y y x
z
( )
(A4.1c)
d x
dt
e
m
B
dy
dt
B
dz
dt
z y
2
2
=
−
−
(A4.2a)
d y
dt
e
m
B
dz
dt
B
dx
dt
x z
2
2
=
−
−
(A4.2b)
d z
dt
e
m
B
dx
dt
B
dy
dt
y x
2
2
=
−
−
(A4.2c)
Assume that a uniform magnetic eld B = B
0
a
z
is the only eld present
(i.e., B
x
= B
y
= 0). Further an electron is assumed to enter the eld at t = 0 at
x = y = z = 0 with an initial velocity U = U
y0
a
y
. As U
z
= 0, z = 0 for all times.
Also U
x
= 0 at t = 0. In view of these assumptions Equation A ...