A thin circular wire carrying current I has magnetic moment M . The shape of the wire is changed to a square and it carries the same current. It will have magnetic moment M₁ . The ratio M to M₁ is

Step-by-step solution

Let the length of the wire be L . For the circular wire of radius r , the circumference is L = 2 r r = L 2 . The magnetic moment of the circular loop is M = I A_c = I ( r^2) = I ( L 2 )^2 = I L^2 4 . For the square wire of side a , the perimeter is L = 4a a = L 4 . The magnetic moment of the square loop is M₁ = I A_s = I (a^2) = I ( L 4 )^2 = I L^2 16 . The ratio of the magnetic moments is M M₁ = I L^2 4 I L^2 16 = 16 4 = 4 . Answer: 4