Fundamentals of Plasma Physics

270 Chapter 9. MHD equilibria

by assigning a magnetic ‘pressure’ proportional toB^2 acting in the direction perpendicular

toB. BecauseB^2 is stronger on the inside of the loop than on the outside, there is a

larger magnetic pressure on the inside. The outward force due to this pressure imbalance is

consistent with the hoop force.

perspective view

of currentloop

top view

ofcurrent loop

B

B

I

I

Figure 9.5: Perspective and top view of magnetic fields generated by a current loop.

The combined effects of magnetic pressure and tension can be visualized byimagining

a current-carrying loop where the conductor has a finite diameter. Suppose that this loop

initially has the relative proportions of an automobile tire, as shown inFig.9.6. The hoop

force will cause the diameter of the loop to increase, while the pinch force will cause the

diameter of the conductor to decrease. The net result is that these combined forces will

cause the automobile tire to evolve towards the relative proportions of a bicycle tire (large

major radius, small minor radius).

‘auto tire ’

‘bicycle tire ’

Figure 9.6: Magnetic forces act to transform a fat small current loop (autotire) into a large
skinny loop (bicycle tire)