Two coils are wrapped around a cylindrical form in such a way that the same flux passes...

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 N₁ turns and the secondary has N₂ (Fig. 7.57). If the current I in the primary is changing, show that the emf in the secondary is given by

where E₁ 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. If you think this violates the conservation of energy, study Prob. 7.58.]

figure 7.57