Magnetism
155
19.32
Since the centripetal acceleration is furnished by the magnetic force acting on the ions,
2
mv
qvB
r
=
or the radius of the path is
mv
r
qB
=
. Thus, the distance between the impact
points (that is, the difference in the diameters of the paths followed by the
U
and the
isotopes) is
238
235
U
(
)
(
)
(
)
(
)
(
)
(
)
238
235
238
235
5
27
19
2
2
2 3.00
10 m s
kg
238 u
235 u
1.66
10
u
1.60
10
C
0.600 T
v
d
r
r
m
m
qB
−
−
∆
=
−
=
−
×
=
−
×
×
or
2
3.11
10
m
3.11 cm
d
−
∆
=
×
=
19.33
In the perfectly elastic, headon collision between the
particle
α
and the initially
stationary proton, conservation of momentum requires that
m v
0
m v
m v
α
α
α
p
p
+
=
while
conservation of kinetic energy also requires that
(
)
or
p
p
v
v
α
α
0
0
v
0
v
v
v
−
= −
−
=
+
. Using
the fact that
4
p
m
m
α
=
(
)
and combining these equations gives
(
)
(
)
0
0
4
or
p
p
p
m
v
m
v
m
v
α
α
=
0
4
v
+
+
3
5
v
v
α
=
and
(
)
0
0
0
3
5
8
5
p
v
v
v
v
=
+
=
Thus,
0
3
3
5
3
5
5
8
8
p
p
v
v
v
v
=
=
=
α
After the collision, each particle follows a circular path in the horizontal plane with the
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 Spring '09
 Physics, Electron, Magnetism, Acceleration, Force, Momentum, Work, Magnetic Field, Righthand rule

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