Physics 105B Problem Set 9
June 3, 2008
Je
ff
Schonert:
schonert (at) physics.ucsb.edu
Taylor 15.80
Refer to the equation of motion listed in problem 15.79:
F
=
γ
m
a
+ (
F
·
v
)
v
/c
2
Since the magnetic force is perpendicular to both
v
and
B
, this means that
F
·
v
= 0 We
also know that magnetic forces cannot change the speed of a particle; they can only change
its direction. Therefore,
v
is a constant, meaning that
γ
is a constant as well. Plugging these
into the above force equation, we get that
γ
m
˙
v
=
e
(
v
×
B
)
This is the same as the nonrelativistic equation except now
m
has been replaced by
γ
m
.
So the physics of the particle is basically the same, with this minor mass modification.
Therefore, if
v
is initially orthogonal to
B
, then it will stay orthogonal. This perpendicular
force will result in circular motion with radius
r
=
γ
mv
eB
=
p
eB
Taylor 15.87
Let the pion initially be traveling along the
x
axis, so that the two photons are traveling in
the
xy
plane. Initial 4momentum is denoted
p
π
and the two final 4momenta are
p
1
and
p
2
.
Conservation of momentum requires that
p
π
=
p
1
+
p
2
. Because the pion has no momentum
in the
y
direction, its 4momentum is
(
E
π
/c,
p
π
,
0
,
0)
,
meaning that the
y
momenta of the two photons must add up to zero in order to have
conservation of momentum. Therefore,
p
y
1
=

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 Spring '08
 MARTINIS
 mechanics, Force, Momentum, Fundamental physics concepts, wave equation

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