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A plasma is a gas of ionized (charged) particles. When plasma is in motion, magnetic effects “squeeze” its volume, inducing inward pressure
Question
A plasma is a gas of ionized (charged) particles. When plasma is in motion, magnetic effects “squeeze” its volume, inducing inward pressure known as a pinch. Consider a cylindrical tube of plasma with radius R and length L moving with velocity v along its axis. If there are n ions per unit volume and each ion has charge q , we can determine the pressure felt by the walls of the cylinder.
Required:
a. What is the volume charge density p in terms of n and q?
b. The thickness of the cylinder surface is n^1/3. What is the surface charge density σ in terms of n and q?
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Physics
3 years
2021-09-03T00:58:33+00:00
2021-09-03T00:58:33+00:00 1 Answers
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Answers ( )
Answer:
a
The volume charge density is![Rendered by QuickLaTeX.com \rho = nq](https://documen.tv/wp-content/ql-cache/quicklatex.com-061b10415bb4f9b9de977f9e186c4266_l3.png)
b
The surface charge density is![Rendered by QuickLaTeX.com \sigma = n^{\frac{2}{3} } q](https://documen.tv/wp-content/ql-cache/quicklatex.com-6eb7f909eb36b80b19e2a9b9288c40a7_l3.png)
Explanation:
From the question we are told that
The radius is R
The length is L
The velocity is v
The number of ions per unit volume is n
The charge is q
The thickness of the cylinder surface is![Rendered by QuickLaTeX.com n^{\frac{1}{3} }](https://documen.tv/wp-content/ql-cache/quicklatex.com-749424f6159258de4bc3f78362441c19_l3.png)
The volume charge density is mathematically represented as
The surface charge density is mathematically represented as
substituting for![Rendered by QuickLaTeX.com \rho](https://documen.tv/wp-content/ql-cache/quicklatex.com-da039068127cf2ec5fc05123d4d3546f_l3.png)