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55. Using the classical orbital radius formula
0
/ 
rm
vq
B
=
, the period is
00
2/2/


.
Tr
v
m
q
B
π
=
=
In the relativistic limit, we must use
0

pm
v
rr
qB qB
γ
===
which yields
0
22
TT
B
==
=
(b) The period
T
is not independent of
v
.
(c) We interpret the given 10.0 MeV to be the kinetic energy of the electron. In order to
make
use
of
the
mc
2
value
for
the
electron
given
in
Table
373
(511 keV = 0.511 MeV) we write the classical kinetic energy formula as
Km
v
m
c
v
c
mc
classical
F
H
G
I
K
J
=
1
2
1
2
1
2
2
2
c
h
c
h
β
.
If
K
classical
= 10.0 MeV, then
=
2
2100
0511
6 256
2
K
mc
classical
MeV
MeV
.
.
.,
bg
which, of course, is impossible (see the Ultimate Speed subsection of
§372). If we use
this value anyway, then the classical orbital radius formula yields
()
( ) ( )
31
8
3
19
9.11 10
kg
6.256
2.998 10 m/s
4.85 10 m.
1.6 10
C
2.20T
mv
m c
r
qB
eB
−
−
−
××
=
×
×
(d) Before using the relativistically correct orbital radius formula, we must compute
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 Spring '08
 Any
 Physics

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