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## Kinematics (and Dynamics) of Magnetic Fields in Plasmas

Depending on the order of magnitude of magnetic field, plasma conductivity, and flow properties, the magnetic field interaction with the plasma can demonstrate aspects of diffusion and convection (Cowling, 1957; Boyd and Sanderson, 1969). To examine this behavior, we consider the governing equations and some limiting cases.
We had seen above that Faraday's law can be expressed as:

$∂B→∂t=−∇×E→=−∇×[J→σ−v→×B→+ΩeBσ(J→×B→)],and∂B→∂t=−∇×[∇×B→μσ−v→×B→+ΩeBσ(J→×B→)].$

Now let us take: $J→×B→≈0$. Then we have: ...

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