7 August 2016
Revision of Question One
1. What is the best way to win an argument?
In order to answer this question properly I need to know what one would describe winning as. Could it be described as being
Physics 525 - Homework 5 Solutions
1 Strongly magnetized plasmas
The dielectric tensor for a cold plasma is
Taking the limit ce,ci pe,pi , will simplify the expressions in the dielectric tensor in the following ways:
Physics 525 - Homework 1 Solutions
Debye lengths for electrons and ions (protons):
ne 3 , Nde =
for the plasma parameter, N = n3 is also acceptable.
Physics 525 - Homework 2 Solutions
Earth's Magnetic Field
The magnetic eld above the equator is of the form
B(r) = B0
where the sign comes in because the magnetic eld points from south to
north and the magnitude has been normalized so that
Physics 525 - Exam I Solutions
The rst adiabatic invariant = V /(2B) is conserved if B is changing slowly.
Let the initial velocty of the proton be V0 (it is given that V0 = 0).
1) Change B from 0.1T to 1T : V1 = 10V0 ;
Physics 525 - Homework 3 Solutions
Linearized equations of motion, for species = cfw_e, i
= q E
ns qs , n = n0 + n
v = 0
In Fourier space, these become
im v = q E
ns q s
i + in0 k v = 0
Take k (1), a
Physics 525 - Homework 7 Solutions
1 Two-stream instability
For a species moving with velocity v0 , we have the momentum evolution
m n0 [
)v1 ] = q n0 E
im n0 v1 + ikv0 m n0 v1 = q n0 E
m ( kv0 )
The continuity equation:
Physics 525 - Homework 6 Solutions
The equation describing recombination is given by
Solving this dierential equation with the initial condition n(0) = n0 =
1020 m3 will yield the following equation
Physics 525 - Exam III Solutions
a) Two kinds of waves: Electron plasma waves (Langmuir waves) and EM waves.
No ion-acoustic waves, since Te Ti .
b) Only Lagnmuir waves, since EM waves have phase velocity larger than speed
of light, and no parti
March. 6, 2012
Problem 1. Magnetic Pumping
A 1-Kev proton with V=0 in a uniform magnetic field B=0.1T is accelerated as B is slowly
increased to 1T. It then makes an elastic collision with a heavy particle and changes direction so
May 10, 2012
Consider a uniform, isotropic, non-magnetized, fully ionized collisionless plasma with
a) What waves can propagate in such a plasma? (derivation of dispersion relations is not required.)
b) What waves will be aff
Physics 525 - Exam II Solutions
a) Use the formula
B(z)ne (z)dz 1.5 1011 Bne L.
Substituting = 0.01m, ne = 1012 cm3 , and L = 0.5m, we nd B 0.12T.
b) One can measure how the rotation angle of the polarization pl
April 24, 2012
The plane of polarization of an electromagnetic wave with frequency
along the magnetic field through a uniform plasma (
cm ), rotates by
m of plasma.
a) What is the strength of
Homework 4 Solutions
A point dipole with dipole moment p is located at the point x0 . From the properties of the derivative of a
Dirac delta function, show that for calculation of the potential or the energy of a dipo
Homework 2 Solutions
Prove the mean value theorem: For charge-free space the value of the electrostatic potential at any point is
equal to the average of the potential over the surface of any sphere centered on that
Homework 5 Solutions
A right-circular solenoid of nite length L and radius a has N turns per unit length and carries a current I.
Show that the magnetic induction on the cylinder axis in the limit N L is
0 N I
Homework 6 Solutions
In three dimensions the solution to the wave equation (6.32) for a point source in space and time (a light
ash at t = 0, x = 0) is a spherical shell disturbance of radius R = ct, namely the Green
Midterm 1 Solutions
Two conducting spheres of radius a, one charged and the other neutral, are placed distance d a apart.
Find the force between the spheres, if the chage on the rst sphere is Q.
The neutral sphere will be plarize