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

a

The volume charge density is
`\rho = nq`

b

The surface charge density is
`\sigma = n^{(2)/(3) } q`

Step-by-step 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^{(1)/(3) }`

The volume charge density is mathematically represented as

`\rho = nq`

The surface charge density is mathematically represented as

`\sigma = \rho n^{(1)/(3) }`

substituting for
`\rho`

`\sigma = n * n^{(1)/(3) } q`

`\sigma = n^{(2)/(3) } q`