A thin straight bar magnet of magnetic moment M is bent into an arc of a circle. If the new magnetic moment of the bent magnet is 2 2 M , the angle subtended by the arc at the centre of the circle is

Step-by-step solution

Let the initial length of the magnet be L and its pole strength be m . The initial magnetic moment is M = m L . When bent into an arc of a circle of radius R subtending an angle (in radians) at the centre, the arc length is L = R R = L . The new effective magnetic length L^ is the straight-line distance (chord) between the poles: L^ = 2R ( 2 ) = 2L ( 2 ) The new magnetic moment is M^ = m L^ = m 2L ( 2 ) = M ( 2 ( 2 ) ) . Given that M^ = 2 2 M , we have: 2 ( 2 ) = 2 2 ( /2) = 2 By checking standard angles, if = 2 (