A uniform conducting wire of length L carrying a steady current I is bent to form a single-turn loop of different geometric shapes. Match the shapes in List-I with their corresponding magnetic dipole moments in List-II. List-I List-II A. Circular loop I. IL^2 16 B. Square loop II. IL^2 4 C. Equilateral triangle III. 3 IL^2 24 D. Regular hexagon IV. 3 IL^2 36 Choose the correct answer from the options given below:

Step-by-step solution

The magnetic dipole moment of a single-turn current loop is given by M = IA , where I is the current and A is the area of the loop. A. Circular loop: Perimeter L = 2 R R = L 2 Area A = R^2 = ( L 2 )^2 = L^2 4 Magnetic moment M = IL^2 4 (Matches II) B. Square loop: Perimeter L = 4a a = L 4 Area A = a^2 = ( L 4 )^2 = L^2 16 Magnetic moment M = IL^2 16 (Matches I) C. Equilateral triangle: Perimeter L = 3a a = L 3 Area A = 3 4 a^2 = 3 4 ( L 3 )^2 = 3 L^2 36 Magnetic moment M = 3 IL^2 36 (Matches IV) D. Regular hexagon: