Two wires of same length are bent to form the circular loop with two turns and a square loop of one turn. Both of them carry same current. The ratio of magnetic moment of circular loop of two turns to that of square loop is

Step-by-step solution

Let the length of the wire be L and the current be I . For the circular loop with two turns, the total length is 2 2 r = L , which gives r = L 4 . The magnetic moment of the circular loop is M₁ = N₁ I A₁ = 2 I ( r^2) = 2 I ( L 4 )^2 = I L^2 8 . For the square loop with one turn, the perimeter is 4a = L , which gives a = L 4 . The magnetic moment of the square loop is M₂ = N₂ I A₂ = 1 I a^2 = I ( L 4 )^2 = I L^2 16 . The ratio of their magnetic moments is M₁ M₂ = I L^2 8 I L^2 16 = 16 8 = 2 . Answer: 2 :