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

8

$L = \mu_0 N^2 A/l = \mu_0 (N/l)^2 Al$

            Here (N/l) remains unchanged. When linear dimensions are increased by a factor 2, area becomes 4 times and the length becomes two times. Therefore, the coefficient of self induction becomes 8 times.