On both sides of a magnetic needle, two short magnets A and B are placed on the same horizontal line which is perpendicular to the magnetic meridian. The south poles of A and B are facing each other, which are 10 cm and 20 cm respectively from the magnetic needle. If the needle remains undeflected, the ratio of the magnetic moment of A to that B is:

Step-by-step solution

The magnetic field due to a short magnet on its axial line at a distance d is given by B = ₀ 4 2M d^3 . Since the magnetic needle remains undeflected, the magnetic fields produced by magnets A and B at the position of the needle must be equal and opposite. B_A = B_B ₀ 4 2M_A d_A^3 = ₀ 4 2M_B d_B^3 M_A M_B = ( d_A d_B )^3 Given d_A = 10 cm and d_B = 20 cm . M_A M_B = ( 10 20 )^3 = 1 8 The ratio of the magnetic moment of A to that of B is 1:8 . Answer: 1:8