A straight steel wire of length L acts as a magnet with a magnetic moment M . It is then bent at its midpoint such that its new magnetic moment becomes 3 M 2 . The angle between the two arms of the bent wire is:

Step-by-step solution

The initial magnetic moment of the straight wire is M = m L , where m is the pole strength. When the wire is bent at its midpoint, it forms two arms, each of length L 2 , with an angle between them. The new effective length L' is the straight-line distance between the two ends. Using the cosine rule for the triangle formed by the two arms and the distance between the ends: (L')^2 = ( L 2 )^2 + ( L 2 )^2 - 2 ( L 2 ) ( L 2 ) (L')^2 = L^2 4 + L^2 4 - L^2 2 = L^2 2 (1 - ) The new magnetic moment is given as M' = 3 M 2