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in Physics by (65.1k points)

A Loop carrying current I lies in XY–plane as shown in the figure. The unit vector k˄ is coming out of the plane of the paper. The magnetic moment of the current Loop is ______

(a) Ia2k

(b) [(π/2) + 1]a2 I k

(c) – [(π/2) + 1]a2Ik

(d) (2π + 1)a2 Ik

1 Answer

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Best answer

The correct option  (b) [(π/2) + 1]a2 I k

Explanation:

A1 = area of central square = (side)2 = a2

A2 = area of all focus semicircles = 4 × (πr2/2) = 2πr2

Here radius = (a/2)

Hence A2 = 2π(a/2)2 = 2π × (a2/4) = (πa2/2)

∴  Total area = A1 + A2 = a2 + (π/2)a2 = a2[1 + (π/2)]

Magnetic moment = M = IA = Ia2[1 + (π/2)]k

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