A short straight bar magnet of magnetic moment M produces a magnetic field B at a large distance d on its axial line. If this magnet is now bent into a semicircle, what will be the new magnetic field at the same distance d on the new axial line?

Step-by-step solution

The magnetic field produced by a short bar magnet of magnetic moment M on its axial line at a large distance d is given by: B = ₀ 4 2M d^3 When the straight magnet of length L is bent into a semicircle of radius R , the length of the arc is L = R , which gives R = L . The new effective length of the magnet is the shortest distance between its poles, which is the diameter 2R = 2L . Since the pole strength m remains unchanged, the new magnetic moment M' is: M' = m (2R) = m 2L = 2(mL) = 2M The new magnetic field B' at