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Consider a circular current-carrying loo...

Consider a circular current-carrying loop of radius R in the x-y plane with centre at origin. Consider the line integral `zeta(L)=|int_(-L)^(L)vecB.dvecl|` taken along z-axis.
(a) Show that `zeta(L)` monotonically increases with L.
(b) Use an appropriate Amperian loop to show that `zeta(oo)=mu_0I`, where I 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 `zeta(L)` and `zeta(oo)`?

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