Two coils C₁ and C₂ are kept coaxially as shown the coil C₁ is connected to a battery and the coil C₂  is connected to a galvanometer. The deflection in galvanometer can be increased by

$$\begin{gathered} \mathrm{Induced} \mathrm{current} \mathrm{i} = \frac{\mathrm{d\varphi }}{\mathrm{dt}}\frac{1}{\mathrm{R}} \\ \mathrm{Here} \mathrm{\varphi } \mathrm{is} \mathrm{the} \mathrm{flux} \mathrm{linked} \mathrm{with} {\mathrm{C}}_2 \mathrm{produced} \mathrm{due} \mathrm{to} \mathrm{current} \mathrm{in} {\mathrm{C}}_1. \\ \mathrm{If} \mathrm{a} \mathrm{soft} \mathrm{iron} \mathrm{core} \mathrm{is} \mathrm{inserted} \mathrm{magnetic} \mathrm{flux} \mathrm{increases}, \mathrm{increase} \mathrm{in} \mathrm{current} \\ \mathrm{in} {\mathrm{C}}_1 \mathrm{also} \mathrm{increases} \mathrm{\varphi } \mathrm{and} \mathrm{increasing} \mathrm{relative} \mathrm{speed} \mathrm{also} \mathrm{increase} \mathrm{\varphi }. \\ \mathrm{Hence} \mathrm{all} \mathrm{the} \mathrm{three} \mathrm{cases} \mathrm{induce} \mathrm{current} \mathrm{increases}. \end{gathered}$$