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A wire of length 4.4 m is bent round in the shape of a circular loop and carries a current of 1.0 A . The magnetic momen…

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A wire of length 4.4 m is bent round in the shape of a circular loop and carries a current of 1.0 A . The magnetic moment of the loop will be :

a

\(0.7{\mathrm{Am}}^{2}\)

b

\(1.54{\mathrm{Am}}^{2}\)

c

\(2\cdot 10{\mathrm{Am}}^{2}\)

d

\(3\cdot 5{\mathrm{Am}}^{2}\)

✓ Correct answer: b)

\(1.54{\mathrm{Am}}^{2}\)

Explanation

The magnetic moment M of a current-carrying loop is given by:M=IA,
where I is the current and A is the area of the loop. The area of a circular loop is:A=π\({r}^{2}\).
The circumference of the loop is 2πr=4.4m,

so:r=\(\frac{4.4}{2\pi }\)=0.7m.


Now, calculating the area:A=π(\(0.{7}^{2}\))=1.54
Thus, the magnetic moment is:M=1.0×1.54=1.54A\({m}^{2}\).

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