The magnetic field created by a large current passing through plasma (ionized ga

Question

The magnetic field created by a large current passing through plasma (ionized gas) can force current-carrying particles together. This pinch effect has been used in designing fusion reactors. It can be demonstrated by making an empty aluminum can carry a large current parallel to its axis. Let R represent the radius of the can and I the current, uniformly distributed over the can's curved wall. (a) Determine the magnetic field just inside the wall. (Use any variable or symbol stated above along with the following as necessary: mu0.) magnitude B = [ ] (b) Determine the magnetic field just outside. (Use any variable or symbol stated above along with the following as necessary: mu0 and pi.) magnitude B = (c) Determine the pressure on the wall. (Use any variable or symbol stated above along with the following as necessary: mu0 and pi.) magnitude P =

Explanation / Answer

PART A:

0 T, as there is no enclosed current.

PART B:

It is just the same as a single wire of charge I at this radius,

B = [uo I] / [2 pi R] [ANSWER]

PART C:

P = BIL/[2 pi r L]

= B I / [2 pi R]

P = uo I^2 / [4 pi^2 R^2] [ANSWER]

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