Consider a circular current-carrying loop of radius R in the x-y plane with center at the origin. Consider the line integral taken along the z-axis.
(a) Show that (L) monotonically increases with L.
(b) Use an appropriate Amperian loop to show that (∞) = , where l is the current in the wire.
(c) Verify directly the above result.
(d) Suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about (L) and (∞)?
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