Physics 5422 Magnetospheric Physics
Spring 1998, R. L. Lysak
Problem Set 1
(Due: April 10, 1998)
- Using the field line equation, write the magnitude of the dipole field in
terms of (a) the L parameter and the radial distance r; and (b)
L and the latitude l (eliminating r).
(Problem 3.3 of Parks) Show that the
arc length of a dipole field line is given by:
Note that the arc length can be defined (in Cartesian coordinates) by:
- Suppose that the IMF is southward, with a magnitude of 10 nT. Calculate
the invariant latitude of the separatrix for the Earth's dipole field using
- (Problem 3.14 of Parks) Show that the vector potential for a dipole field
can be written in terms of its azimuthal (j) component as:
Show that lines of constant Aj
are always perpendicular to the magnetic field line.
- Consider a Harris field geometry of the form
Determine the current density (magnitude and direction) and the plasma pressure
distribution for this equilibrium.