A straight bar magnet has a magnetic moment M . It is first cut transversely into two equal halves. One of these halves is then bent into the shape of a semicircle. The magnetic moment of this bent half will be

Step-by-step solution

Let the initial length of the bar magnet be L and its pole strength be m . The initial magnetic moment is M = mL . When the magnet is cut transversely into two equal halves, the length of each half becomes L 2 . The pole strength m remains unchanged. When one of these halves is bent into a semicircle of radius R , the arc length is equal to the length of the piece: R = L 2 R = L 2 The new effective magnetic length is the shortest distance between the poles, which is the diameter of the semicircle: d = 2 R = 2 ( L 2