December 2014
Intermediate to advanced
418 pages
16h 17m
English
Content preview from Electricity and Magnetism
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Chapter 27
Back to Moving Charged Particles
Consider a particle with mass m, charge q, and velocity ~v, moving through a region of space
containing a uniform magnetic field,
→
B
0
. The Lorentz force acting on the particle is
→
F
M,q
= q ~v ×
→
B
0
.
Recall that the Lorentz force does no work on the charged particle.
[The force is always orthogonal to the particle’s velocity.]
Provided that there are no other forces acting [or the other forces all precisely cancel], the
kinetic energy of the particle remains constant.
1
Without any loss of generality, let’s choose coordinates such that the z-axis lines up with
the magnetic field, so
→
B
0
= B
0
ˆ
k. Further suppose that
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