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1answer
13 views

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}) + ...
2
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1answer
36 views

ϕ-component of equation of moition: proving a relationship [closed]

I have the following velocity vector (in spherical polars): \begin{equation} \textbf{v} = u \hat{\textbf{r}} + v_{\phi}\hat{\boldsymbol\phi} \end{equation} Where $u(r) = u$ and $v_{\phi} (r) = ...
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0answers
10 views

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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0answers
26 views

Interpretation of Mass Continuity Equation in MHD [duplicate]

I'm writing up my final-year dissertation and I'm required to give, as part of the introduction, an analysis of all the equations (and their terms) of which I use. Embarrassingly, whilst of course ...
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0answers
43 views

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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1answer
108 views

Why doesn't magnetic forces on current carrying wire depends on relative velocity?

We know that magnetic field arises due to relative velocity of charged particle . Electrons in wire move at very slow drift velocity but relativistic variation of magnetic field doesn't seem to apply ...
0
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1answer
163 views

Alternative air transportation and magneto-aerodynamics

Firstly, I am not a big fan of UFOs, however, a flying saucer makes me think if is there another, comparatively agile way to travel through the air without jets, turbines or propellers (balloons are ...
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0answers
82 views

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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0answers
55 views

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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0answers
76 views

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, ...
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5answers
2k views

Why do we deal only with large scale magnetic fields in astrophysics, and not electric fields?

In astrophysics there is a lot going on about strong, large scale magnetic fields: in stars (prominences), magnetic dynamos, compact accretors collimating jets, etc. There's even a special ...
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1answer
55 views

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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2answers
137 views

Why does this equation refer to magnetic tension?

The force density in a plasma, according to MHD, is $$ \mathbf{F} = -\nabla P -\nabla(\frac{B^2}{2\mu_0}) + \frac{1}{\mu_0}(\mathbf{B}\cdot\nabla)\mathbf{B} $$ where first term is the thermal ...
4
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1answer
329 views

Application of Ampère's law in low $Re_m$ MHD

Ampère's law states that $$ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} \tag{1}$$ Simultaneously, from Ohm's law, we know that ...
3
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1answer
313 views

Why closed bottle change its weight when I put effervescence tablet?

I use several shape, several type of material (glass, metal, plastic), I use two different balances with 0.01g of accuracy. I put oil on gasket, and put upside down (like that I can see if water ...
1
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1answer
354 views

Lorentz force for electrically conducting fluid flow in homogeneous magnetic field

I am mathematician and have paper which models situation when homogeneous magnetic field is applied to moving electrically conducting fluid. There is such Lorentz force formula on which all the work ...
3
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1answer
210 views

A rod filled with water and charged particles is rotated in magnetic field

Assume we have a rod of diameter $d$ and length $l$. It is filled with a mixture of water and, say, sodium chloride. Thus there are positively charged sodium ions and negatively charged chloride ions ...
1
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1answer
328 views

The equation of a ferrofluid under a magnetic field?

What is the parametric equation guiding the geometry of a ferrofluid under a magnetic field? See also this Wikipedia page. From previous research, Maxwell's Equations and Navier-Stokes Equations were ...
3
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0answers
31 views

Richtmyer Meshkov instability in MHD [duplicate]

Possible Duplicate: Richtmyer Meshkov instability in MHD The Richtmyer Meshkov instability in Hydrodynamics:- 1) When shock wave interacts with the contact discontinuity, it accumulates the ...
3
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1answer
159 views

Richtmyer Meshkov instability in MHD

In magnetohydrodynamics, the Richtmyer Meshkov instability is found to get suppressed by application of longitudinal magnetic field. Exactly what happens at the interface? Why instability gets ...
2
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0answers
233 views

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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2answers
205 views

Dynamic ferrofluid sculptures

http://www.youtube.com/watch?v=UJJuq_pcyIQ What exactly is going on in the video example? I understand the phenomena occurs because of magnetism but I am trying to figure out the mechanics behind ...
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5answers
3k views

What sustains the rotation of earth's core (faster than surface)?

I recently read that the earth's core rotates faster than the surface. Well, firstly, it's easier to digest the concept of planetary bodies, stars, galaxies in rotation and/or orbital motion. But, ...
3
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2answers
383 views

Producing energy from magnetic flux loops

I've simplified this down by quite a lot but as far as I understand it, magnetic fields on the Sun's surface twist together and when it gets all a bit too much they release energy. My question is why ...
5
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4answers
672 views

Help fill in my understanding of the Polywell fusion reactor

Polywell is a proposed new type of fusion reactor, which is designed to use magnetic fields to overcome the problems with the Elmore-Tuck-Watson fusor. I'm trying to understand exactly how it works. ...
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3answers
690 views

How can we make an order-of-magnitude estimate of the strength of Earth's magnetic field?

The source of Earth's magnetic field is a dynamo driven by convection current in the molten core. Using some basic physics principles (Maxwell's equations, fluid mechanics equations), properties of ...