# NCERT Physics Class 12 Exemplar Ch 4 Moving Charges and Magnetism Part 6

Q.26 A uniform conducting wire of length and resistance is wound up as a current carrying coil in the shape of

(i) An equilateral triangle of side ;

(ii) A square of sides and,

(iii) A regular hexagon of sides .

The coil is connected to a voltage source . Find the magnetic moment of the coils in each case.

Solution:

Area:

Current is same for all

Magnetic moment

(Note: is in a geometric series)

Q.27 Consider a circular current-carrying loop of radius in the plane with center at origin. Consider the line integral taken along axis.

(a) Show that monotonically increases with L.

(b) Use an appropriate Amperian loop to show that , where 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 carrying the same current . What can you say about and ?

Solution:

(a) Points in the same direction on axis and hence is a monotonically increasing function of .

(b) Contribution from large distance on contour

Contribution from large distance

(C)

Put

(d)

But by using arguments as in (b)

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