A coil is wound as a transformer of rectangular cross-section. If all the linear dimensions of the transformer are increased by a factor 2 and the number of turns per unit length of the coil remain the same, the self  inductance increased by a factor of                  

     Self inductance L= μ₀ N² A / l = μ₀ n² lA

     Where n is the number of turns per unit length and N is the total number of turns and

     In the given question n is same. A is increased 4 times and l is increased 2 times and hence L will be increased 8 times.