Magnetohydrodynamics - Derivation of PDE

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SUMMARY

The discussion focuses on deriving the partial differential equation (PDE) that describes the potential distribution φ in a stationary electrolyte influenced by a magnetic field "B" and a current density "j" in a two-dimensional space. The derivation begins with the principle of charge balance within the system. The conversation also highlights the need for proper categorization of homework-related queries within the forum.

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  • Understanding of magnetohydrodynamics principles
  • Familiarity with partial differential equations (PDEs)
  • Knowledge of charge conservation in electromagnetic fields
  • Basic concepts of stationary electrolytes and current density
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  • Study the derivation of PDEs in magnetohydrodynamics
  • Explore charge conservation laws in electromagnetic theory
  • Learn about the effects of magnetic fields on current densities
  • Investigate applications of PDEs in fluid dynamics
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Students and researchers in physics, particularly those focusing on magnetohydrodynamics, as well as educators looking for insights into teaching PDE derivations in electromagnetic contexts.

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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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Is this a homework problem?
 
jasonRF said:
Is this a homework problem?
Yes. Is it in the wrong forum part?
 
Yes. There is a separate homework section. I have asked the moderators to move this thread over there.
 
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