A straight bar magnet has a magnetic moment M . Match the different shapes into which it is bent (List-I) with its new magnetic moment (List-II). List-I List-II (A) Bent at midpoint at 90^ (I) 0 (B) Bent at midpoint at 120^ (II) 2M (C) Bent into a semicircle (III) M 2 (D) Bent into a complete circle (IV) 3 M 2 Choose the correct answer from the options given below:

Step-by-step solution

Let the original length of the magnet be L and its pole strength be m . The initial magnetic moment is M = mL . (A) When bent at the midpoint at 90^ , the two arms each have length L/2 . The new effective length is the hypotenuse: L' = (L/2)^2 + (L/2)^2 = L 2 . New magnetic moment M' = m L 2 = M 2 . (Matches III) (B) When bent at the midpoint at 120^ , the distance between the poles is L' = 2 ( L 2 ) ( 120^ 2 ) = L 60^ = 3 L 2 . New magnetic moment M' = m 3 L 2 = 3 M 2 . (Matches IV) (C) When bent into a semicircle