Combine 3 Eqns for Plasma in a Solenoid

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SUMMARY

The discussion focuses on the combination of three equations related to plasma behavior in a solenoid. The equations include the current density equation ∇p=j×B, the relationship K=nI, and the solenoid magnetic field equation BSolenoid=μnI. The final combined equation derived is j=-2p0r/(a2μK) in the θ hat direction. The participants confirm the correctness of the derivation, indicating that the approach is valid and complete.

PREREQUISITES
  • Understanding of plasma physics and magnetohydrodynamics
  • Familiarity with vector calculus and differential equations
  • Knowledge of solenoid magnetic field principles
  • Basic concepts of current density and pressure in plasma
NEXT STEPS
  • Research the implications of the derived equation j=-2p0r/(a2μK) on plasma stability
  • Explore the role of magnetic fields in plasma confinement techniques
  • Study the application of magnetohydrodynamics in fusion reactors
  • Investigate advanced solenoid designs for improved plasma control
USEFUL FOR

Physicists, engineers, and researchers working in plasma physics, particularly those focused on magnetic confinement and fusion technology.

ccab521
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Homework Statement
See Attached file
Relevant Equations
See Attached file
∇p=j×B (eq. 1)
K=nI
BSolenoid=μnI⇒μK (eq. 2)
∇p=-2p0r/(a2) (eq. 3)
Combining these three equations:
j=-2p0r/(a2μK) (θ hat direction)

Feel like this is too simple and might be missing a step any help would be much appreciated!
 

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Your work looks correct to me.
 
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