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 particle 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 well. (a) Determine the magnetic field just inside the wall. (use any variable or symbol stated above along with the following as necessary:) magnitude direction (b) Determine the magnetic field just outside. (Use any variable or symbol stated above along with the following as necessary) magnitude direction (c) Determine the pressure on the wall (use any variable or symbol stated above along with the following as necessary) magnitude direction

Explanation / Answer

(A) using Ampere's law,

B.(2 pi r ) = u0 Iin

for just inside the wall, Iin = 0

B = 0

(B) for just outside the wall,

Iin = I

B (2 pi R) = u0 I

B = u0 I / (2 pi R)

(c) F = I L B

A = 2 pi r L

P = F / A

= ( I L B) / (2 pi R L)

= I B / (2 pi R)

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