A uniform conducting wire of total length 60L is used to form two separate current-carrying coils. First, the entire wire is wound to form a square coil of side 3L . Later, the same wire is unwound and completely

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Correct answer: B. 15 : 8

Total length of the wire, L_ total = 60L . For the square coil: Side of the square, a = 3L . Perimeter of one turn = 4a = 12L . Number of turns, N_1 = (60L)/(12L) = 5 . Area of one turn, A_1 = a^2 = 9L^2 . Magnetic dipole moment, M_1 = N_1 I A_1 = 5 × I × 9L^2 = 45 I L^2 . For the rectangular coil: Length = 4L , width = L . Perimeter of one turn = 2(4L + L) = 10L . Number of turns, N_2 = (60L)/(10L) = 6 . Area of one turn, A_2 = 4L × L = 4L^2 . Magnetic dipole moment, M_2 = N_2 I A_2 = 6 × I × 4L^2 = 24 I L^2 . Ratio of the magnetic dipole moments: (M_1)/(M_2) = (45 I L^2)/(24 I L^2) = (15)/(8) . Answer: 15 : 8

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