Consider a circular current-carrying

Question:

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

$\Im(L)=\left|\int_{-L}^{L} B \cdot d l\right|$ taken along z-axis.

(a) show that

$\Im(L)$ monotonically increases with $\mathrm{L}$

(b) use an appropriate Amperian loop to that

(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

Solution:

(a) Magnetic field due to a circular current-carrying loop is given as

It is a monotonically increasing function of L

(b) The Amperian loop is given as

(c) The magnetic field at the axis of the circular coil is given as μ0I

(d) When a circular coil is replaced with a square coil, it is given as

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