Resistive timescale: Difference between revisions

Resistive timescale (view source)

32 bytes added , 12 October 2011

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 The resistive timescale is the typical time for the diffusion of a magnetic field into a resistive plasma.
 Based on Faraday's Law,
-:<math>\frac{d\vec B}{dt} = \vec \nabla \times \vec E,</math>
+:<math>\frac{\partial \vec B}{\partial t} = -\vec \nabla \times \vec E,</math>
 Ohm's Law,
 :<math>\vec E = \eta \vec j,</math>
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 :<math> \vec \nabla \times \vec B = \mu_0 \vec j,</math>
 one immediately derives a diffusion type equation for the magnetic field:
-:<math>\frac{d\vec B}{dt} = \frac{\eta}{\mu_0} \vec \nabla \times \vec \nabla \times \vec B = - \frac{\eta}{\mu_0} \nabla^2 \vec B,</math>
+:<math>\frac{\partial \vec B}{\partial t} = -\frac{\eta}{\mu_0} \vec \nabla \times \vec \nabla \times \vec B = \frac{\eta}{\mu_0} \nabla^2 \vec B,</math>
 since
 : <math>\vec \nabla \cdot \vec B = 0.</math>