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in Physics by (38.8k points)

Consider a circular current-carrying loop of radius R in the x-y plane with centre at origin. Consider the line intergral

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

(b) Use an appropriate Amperian loop to show that ℑ (∞)= μ0I , 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 ℑ(L ) andℑ(∞) ?

1 Answer

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Best answer

(a) B (z) points in the same direction on z - axis and hence J (L) is a monotonically increasing function of L.

(b) J(L) + Contribution from large distance on contour C = μ0I

as L 

Contribution from large distance  0(as B = 1/r3 )

 J() − μ0I

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