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?

Answer 1

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  $\rho$

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

     $\sigma = n^{\frac{2}{3} } q$