![]() For terrestrial planets, this decay period is of order 104 years. In the absence of fluid motions (i.e., v=0), the magnetic field decays over some time period related to the magnetic diffusivity. The second term on the right is called the diffusion term and 1 / (ior) is the magnetic diffusivity. The first term on the right shows that the conducting fluid must be moving with velocity v in order to maintain the magnetic field. (3.32), (3.33), and (3.34) gives the induction equation:Įquation (3.35) shows how the magnetic field B varies with time. Where r is the electrical conductivity of the material and v is the velocity of the conducting fluid. The current (J) induced by the magnetic field is given by Ohm's law: In most planetary magnetic fields, i0e0 (dE/dt) is very small and can be ignored. ![]() Where ^0 is the magnetic permeability of free space (=4p X10-7 N A-2) and e0 is the permittivity of free space (= 8.85X10-12 C2 N-1 m-2). Faraday's law of inductance relates the electric (E) field to a time-varying magnetic (B) field:Īmpère's law describes how currents (J) and time-varying electric fields produce a magnetic field: The basis of MHD analysis is Maxwell's equations.
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