Physics 5422 Magnetospheric Physics

Spring 1998, R. L. Lysak

Problem Set 1

(Due: April 10, 1998)

  1. 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).

  2. (Problem 3.3 of Parks) Show that the arc length of a dipole field line is given by:
  3. Note that the arc length can be defined (in Cartesian coordinates) by:

  4. 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.

  5. (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:
  6. Show that lines of constant Aj are always perpendicular to the magnetic field line.

  7. Consider a Harris field geometry of the form


    Determine the current density (magnitude and direction) and the plasma pressure distribution for this equilibrium.

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