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Chapter 29  2
Magnetic Fields
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View Full Document Magnetic Field
F
B
= q
v
x
B
±
Consider a particle moving
in an external magnetic
field with its velocity
perpendicular to the field
±
The force is always
directed toward the center
of the circular path
±
The magnetic force causes
a centripetal acceleration,
changing the direction of
the velocity of the particle
Force on a Charged Particle
±
Equating the magnetic and centripetal
forces:
±
Solving for
r
:
±
r
is proportional to the momentum of the
particle and inversely proportional to the
magnetic field
2
B
mv
Fq
v
B
r
==
mv
r
qB
=
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View Full Document Motion of Charged Particle
±
The angular speed of the particle is
±
The angular speed,
ω
, is also referred to as
the
cyclotron frequency
±
The period of the motion is
vq
B
ω
rm
==
222
π
r
ππ
m
T
v
ω
qB
===
Motion of a Particle, General
±
If a charged particle
moves in a magnetic
field at some
arbitrary angle
θ
with respect to
B
±
V
=
V
x
i
+
V
y
j
+
V
z
k
22
y
z
vvv
=+
v
x
=
V
cos
θ
=
sin
θ
V
θ
x
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View Full Document Motion of a Particle, General
±
Its path is a helix
22
y
z
vvv
=+
V
x
=
V
cos
θ
= const.
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This note was uploaded on 01/28/2011 for the course PHYS 011 taught by Professor Nianlin during the Fall '08 term at HKUST.
 Fall '08
 NianLin
 Physics, Charge, Force

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