When a current of $5\text{ A}$ passes through the primary coil of a transformer of $200$ number turns, the magnetic flux linked with the secondary coil having $400$ turns is $600 \times 10^{-6}\text{ T m}^2$. Find the induced emf in the secondary coil, when the current in the primary coil increases at a rate of $2\text{ A s}^{-1}$.