NE528 Fall 2009 HW#2 (total 80 points)
Due Wednesday, September 23 by class time
1. (30 points)
A fully ionized, uniform, hydrogen plasma has a density (n
e
= n
i
= n) in orthogonal uniform gravitational
and magnetic fields, where the gravitational field is along y direction
g
= (0,  g, 0), and the magnetic field is
along the z direction
B
= (0, 0, B).
(a) Calculate the drift velocities of each species for the following situations:
(i) In the Earth's magnetosphere at r = 2 R
Earth
, assuming the surface field strength is 10
4
Tesla.
(ii) Near the surface of the Sun in an active region where B = 10
2
Tesla.
(iii) In the magnetosphere of a neutron star at r = 2 R
Sun
assuming the neutron star has the same mass
of the sun and that the surface field strength is 10
8
Tesla at a distance equals to 10
6
cm from the
center of the neutron star.
(b) Check, for each case, the gravitational and Lorentz force acting on the plasma and see if they
cancel out.
Useful
Information:
Radius of the Earth R
Earth
= 10
8.8
cm
Radius of the Sun R
Sun
= 10
10.84
cm
Mass of the earth M
Earth
= 10
27.78
gram
Mass of the Sun M
Sun
= 10
33.3
gram
Surface gravity of the Earth g
Earth
= 10
2.99
cm.s
1
Surface gravity of the Sun g
Sun
= 10
4.44
cm.s
1
Universal gravity equation
2
2
(
, . .
/
)
g
in Newtons i e kg m
s
Mm
F
G
r
=
, where
,
M
is the mass of the object and
m
is the mass of the electron,
r
is the
distance between the electron and the object
(
11
3
2
6.67
10
/
G
m
=
×
)
kg s
Worked Solution
a)
Calculate the drift velocity for each case.
G
B
y
−
x
z
v
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
The case is very similar to the motion of electron in steady electric and magnetic fields.
Universal gravity equation:
2
g
Mm
F
G
r
=
2
(
)
Magnetic
Gravitational
F
q v
B
Mm
G
r
=
+
×
±²³²´
±²³²´
2
2
2
2
2
2
2
2
2
2
2
2
(
)
(
)
0
:
...........................
:
x
x
y
y
y
x
z
x
y
y
x
y
x
dv
m
q v
B
qv B
dt
dv
m
q v
B
dt
dv
m
dt
dv
B
dy
qv
v
v
y
dt
m
dt
dv
d y
m
qv B
dt
dt
Thus
d y
qv B
y
y
oscillatory
dt
Solution
y
Mm
Mm
G
G
r
r
Mm
M
G
G
r
r
M
G
r
M
G
r
ω
ω
ω
ω
ω
⎧
=
×
=
⎪
⎪
⎪
=
+
×
=
−
⎨
⎪
⎪
=
⎪
⎩
=
=
=
⇒
=
=
−
⇒
=
−
+
=
=
1
2
1
2
2
cos
sin
cos
sin
K
t
K
t
dy
K
t
K
t
dt
ω
ω
ω
ω
ω
ω
ω
+
+
= −
+
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 Bourham
 Electron, Magnetic Field, ........., Drift velocity, Lorentz force

Click to edit the document details