Consider a circular current-carrying loop of radius R in the x-y plane with centre at origin. Consider the line integral ζ ( L ) = | ${\int }_{-\mathit{L}}^{\mathit{L}}\mathit{B}.\mathit{d}\mathit{l}$ | taken along z-axis.

(a) Show that ? ( ) monotonically increases with L.

(b) Use an appropriate Amperian loop to show that ζ ( ∞ ) = ?0? , 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 ζ ( L ) and ζ ( ∞ ) ?

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