Two coils $$C_1$$ and $$C_2$$ are placed close to each other. The magnetic flux $$\phi_2$$ linked with the coil $$\mathrm{C}_2$$ varies with the current $$I_1$$ flowing in coil $$C_1$$, as shown in the figure. Find

(i) the mutual inductance of the arrangement, and

(ii) the rate of change of current $$\left(\frac{d \mathrm{I}_1}{d t}\right)$$ that will induce an emf of 100 V in coil C$$_2$$.