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Final

PHYS 4150 Lecture 5: plasma_5Exam


Department
Physics
Course Code
PHYS 4150
Professor
Sascha Kempf
Study Guide
Final

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PHYS4150 — P L A S M A P H Y S I C S
l e c t u r e 5 - s i n g l e pa r t i c l e m o t i o n i n a n u n i f o r m b
f i e l d
Sascha Kempf
G135, University of Colorado, Boulder
Fall 2019
Single particle motion in an uniform B field
1e x a m p l e
Let’s calculate the radius
rm
of a sphere that would be spontaneously depleted of all
electrons due to thermal fluctuations. In this case all electrons previously within the
sphere
Ne=4
3πr3
mn
would move through the outer boundary of the sphere, resulting in a total ion charge
within the sphere of
Q=eNe
. The corresponding electric field
Er
can be found from
Gauss’ law
Q=ǫ0IEdA=ǫ0ErIdA=ǫ0Er4πr2
m,
Er=Q
4πǫ0r2
m
.
Because the energy density of an electric field is
1
2ǫ0E2
, we can can calculate the total
energy resulting from breaking the charge neutrality:
W=
rm
Z
0
1
2ǫ0E24πǫ0r2dr=πr5
m
2n2e2
45ǫ0
.
sascha.kempf@colorado.edu
1
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