Combine 3 Eqns for Plasma in a Solenoid

Thread starter ccab521
Start date Nov 10, 2019
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current plasma pressure solenoid

In summary, a solenoid is a device that uses a coil of wire to create a magnetic field. It can be used to contain and manipulate plasma by applying the Biot-Savart law, Ampere's law, and Faraday's law of induction. These equations can be combined using the principle of superposition to describe the behavior of plasma in a solenoid. This study has many practical applications, including fusion reactors and plasma-based devices, and also helps us understand natural phenomena like solar flares and auroras.

Nov 10, 2019

ccab521

Homework Statement: See Attached file

Relevant Equations: See Attached file

∇p=j×B (eq. 1)
K=nI
B_Solenoid=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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Nov 11, 2019

TSny

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Your work looks correct to me.

Related to Combine 3 Eqns for Plasma in a Solenoid

What is a solenoid?

A solenoid is a coil of wire that is used to create a magnetic field when an electrical current is passed through it.

What is plasma?

Plasma is the fourth state of matter, consisting of a gas of positively and negatively charged particles that are electrically conductive.

How is plasma created in a solenoid?

Plasma can be created in a solenoid by passing a high-frequency alternating current through the coil, causing the electrons in the gas to ionize and form a plasma state.

What are the three equations used to describe plasma in a solenoid?

The three equations used to describe plasma in a solenoid are the continuity equation, the momentum equation, and the energy equation.

How do these equations explain the behavior of plasma in a solenoid?

These equations explain the behavior of plasma in a solenoid by describing the conservation of mass, momentum, and energy in the plasma as it interacts with the magnetic field created by the solenoid.