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MHD Flow in a channel with and external B field and circuitry determining E. Different circuits and Ohm's law

I was wondering if someone can explain why E is the way it is in cases 2,3,4 in page 9 of these notes ? In case 2 "Short Circuit", do I just have to assume that for a perfect conductor E = 0 for ...
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How is the MHD magnetic field time evolution equation transformed to the vector potential time evolution equation?

Starting from the time evolution equation of the magnetic field for incompressible MHD (magnetohydrodynamics) $$\frac{\partial \vec{B}}{\partial t} = \nabla \times (\vec{v} \times \vec{B}) + ...
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Solar wind and the Earth's magnetic field

I have again an old question from a comprehensive exam I took a couple of months ago. Lucky for me one could pick 5 out of 8 questions, because on some of the problems I didn't even know how to start. ...
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Faraday induction for seawater flow system

Magnetic flow meters use Faraday induction to produce a voltage across a channel in which a conductive fluid is flowing. The basic relationship (using convenient geometry so that the cross products ...
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How to solve the following set of equations (magnetohydrodynamics with anomaly term)?

Let's have system of equations: $$ \tag 1 [\nabla \times \mathbf E^{(1)}(\mathbf r , t) ] = -\frac{\partial \mathbf B^{(1)}(\mathbf r , t)}{\partial t} , $$ $$ \tag 2 [\nabla \times \mathbf ...
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MHD stability - boundary conditions

In Freidberg's 'Plasma Physics and Fusion Energy,' ch. 12.4 p 311, right after deriving the Linear Force operator and momentum equation in which it is used $$ -\rho \omega^2 \boldsymbol\xi = ...
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Magnetic fields in plasma at equilibrium

I'm wondering if it is possible to have a plasma reach an equilibrium state where no more entropy is produced but it still has frozen-in magnetic field lines. The problem is the field lines have a ...
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Electrical Resistance of Spherical, Contacting Colloids

So, I work a lot with Magneto-Rheological (MR) fluids - which are essentially electrolyte solutions with suspended, paramagnetic colloids/particles. Once a magnetic field is applied to such a fluid, ...