Question

How does the mutual inductance of a pair coils change when
$\left(i\right)$ distance between the coils is increased and
$\left(ii\right)$ number of turns in the coils is increased?

Answer 1

(i) As $\varphi =MI$, with the increase in the distance between the coils, the magnetic flux marked with the stationary coil decrease and hence the mutual inductance of the two coils will decreases.
(ii) Mutual inductance of two coils can be found out by $\mu n_1{n}_{2}Al$M=μn1n2Al
i.e $M\propto n_1{n}_2$ so with the increase in number of turns mutual inductance increases.