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:
- 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 vacuum superposition.
- (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:
- Consider a Harris field geometry of the form
. Determine the current density (magnitude and direction) and the plasma pressure distribution for this equilibrium.

Note that the arc length can be defined (in Cartesian coordinates) by:

Show that lines of constant *A*_{j}
are always perpendicular to the magnetic field line.