Two short bar magnets A and B are arranged co – axially. The distance between their centres is 30cm. A compass needle placed on their axis at a distance of 6cm from B shows no deflection. The ratio of the magnetic moments of A and B is (Neglect earth’s magnetic field)

Given, distance between the magnets, d = 30cmdompass needle distance from magnet, B = 6cmNow, distance of magnet A from needle, d1=30−6=24 cm and distance of magnet B from needle, d1=6 cm∴  Magnetic field on a axial line is given as, B=μo4π2Md1Hence, the ratio of the magnetic moment for A and BM1d11=M2d21⇒M1M2=(d1d2)3∴  d1=24 cm,  d2=6 cmM1M2=(246)3M1M2=(4)3=64So, the ratio of the magnetic moments of A and B is 64 : 1