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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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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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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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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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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, ...