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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Trung Dũng 3 years 2021-09-03T00:58:33+00:00 1 Answers 11 views 0

Answers ( )

    0
    2021-09-03T00:59:47+00:00

    Answer:

     a

        The volume charge density is  \rho = nq

    b

        The surface charge density is  \sigma =    n^{\frac{2}{3} } q

    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  n^{\frac{1}{3} }

    The volume charge density is mathematically represented as

          \rho =  nq

    The surface charge density is mathematically represented as

        \sigma =  \rho n^{\frac{1}{3} }

    substituting for  \rho

         \sigma =  n *   n^{\frac{1}{3} } q

         \sigma =    n^{\frac{2}{3} } q

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