Two solenoids A and B of equal number of turns have their lengths and radii in the same ratio 1 : 3 . The ratio of the self-inductance of solenoid A to that of B will be

Step-by-step solution

The self-inductance of a solenoid is given by the formula L = ₀ N^2 A l = ₀ N^2 r^2 l Given that the number of turns are equal, N_A = N_B . The ratio of their lengths is l_A l_B = 1 3 The ratio of their radii is r_A r_B = 1 3 Taking the ratio of their self-inductances: L_A L_B = ( r_A r_B )^2 l_B l_A Substituting the given values: L_A L_B = ( 1 3 )^2 ( 3 1 ) L_A L_B = 1 9 3 = 1 3 The ratio of the self-inductance of solenoid A to that of B is 1 : 3 . Answer: 1 : 3