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1
Class Examples for Chapter 28
11.
Since the total force given by
F
e E
v
B
d
i
vanishes, the electric field
E
must be
perpendicular to both the particle velocity
v
and the magnetic field
B
. The magnetic
field is perpendicular to the velocity, so
v
B
has magnitude
vB
and the magnitude of
the electric field is given by
E = vB
. Since the particle has charge
e
and is accelerated
through a potential difference
V
,
2
/2
mv
eV
and
2.
v
eV m
Thus,
19
3
5
27
2 1.60 10
C 10 10 V
2
1.2 T
6.8 10 V m.
9.99 10
kg
eV
EB
m
20.
Combining Eq. 2816 with energy conservation (
eV
=
1
2
m
e
v
2
in this particular
application) leads to the expression
r
=
m
e
e B
2
eV
m
e
which suggests that the slope of the
r
versus
V
graph should be
2
2/
e
m eB
. From Fig.
2839, we estimate the slope to be 5
10
5
in SI units. Setting this equal to
2
e
m eB
and solving we find
B
= 6.7
10
2
T.
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 Fall '08
 IASHVILI
 Force

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