Magnetohydrodynamics - Derivation of PDE

In summary, the conversation is about deriving a partial differential equation (PDE) to describe the potential distribution φ in a system with a stationary electrolyte, a magnetic field "B", and a current density "j" (2D). The speaker is asking for help with this question, which they believe may be a homework problem. They are also asking if the conversation is in the wrong forum section.
  • #1
n0b1
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Summary:: partial differential equation (PDE) to describe the potential distribution φ in the system

Hey, I need some help with the following question:

We have a stationary electrolyte, a magnetic field "B" and a Current density "j" (2D).

Derive the partial differential equation (PDE) to describe the potential distribution φ in the system by balancing the charges first.

1613333524623.png


I don't know how to do anything?
1613333505396.png

https://www.physicsforums.com/attachments/277981
 
Last edited:
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  • #2
Is this a homework problem?
 
  • #3
jasonRF said:
Is this a homework problem?
Yes. Is it in the wrong forum part?
 
  • #4
Yes. There is a separate homework section. I have asked the moderators to move this thread over there.
 
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Likes n0b1

1. What is Magnetohydrodynamics (MHD)?

Magnetohydrodynamics is a branch of physics that studies the dynamics of electrically conducting fluids in the presence of a magnetic field. It combines principles from electromagnetism and fluid mechanics to describe the behavior of plasma, which is a state of matter consisting of charged particles.

2. How are the governing equations of MHD derived?

The equations of MHD are derived from the fundamental principles of conservation of mass, momentum, and energy, along with Maxwell's equations for electromagnetism. These equations are then simplified and combined to form the MHD equations, which are a set of partial differential equations (PDEs) that describe the behavior of a plasma in the presence of a magnetic field.

3. What are the assumptions made in the derivation of MHD equations?

The derivation of MHD equations involves several simplifying assumptions, such as assuming the plasma to be a perfect conductor, neglecting the effects of viscosity and resistivity, and assuming the plasma to be incompressible. These assumptions help to simplify the equations and make them more manageable for analysis and computation.

4. What are the applications of MHD?

MHD has a wide range of applications in various fields, including astrophysics, plasma physics, and engineering. Some specific applications include the study of solar and stellar winds, the design of fusion reactors, and the development of plasma propulsion systems for spacecraft.

5. What are the challenges in solving MHD equations?

Solving MHD equations can be challenging due to the highly nonlinear nature of the equations and the complex interactions between the fluid and magnetic fields. This often requires the use of advanced numerical methods and high-performance computing. Additionally, the large range of scales involved in many MHD problems can also pose challenges in accurately capturing all the relevant physical phenomena.

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