$4$ Deriving the equation for a transformer

Two coils are wrapped around a cylindrical form in such a way that the same flux passes through every turn of both coils. $($In practice this is achieved by inserting an iron core through the cylinder; this has the effect of concentrating the flux.$)$ The primary coil has $N_1$ turns and the secondary has $N_2($Fig$.3).$ If the current I in the primary is changing, show that the emf in the secondary is given by

$\frac{E_2}{E_1}=\frac{N_2}{N_1}$

where $E_1$ is the $($back$)$ emf of the primary.

$[$This is a primitive transformer$-$a device for raising or lowering the emf of an alternating current source. By choosing the appropriate number of turns, any desired secondary emf can be obtained.$]$

Figure $5$: iransiormer.