Ampere's Law, AL. To establish core flux, magnetizing current exists in the primary. The primary is powered by a CVS (constant voltage source). Flux is determined by voltage, frequency, core area, and number of primary turns Np. Open circuited secondary current Is = 0, primary current Ip = exciting current (magnetizing current plus hysteresis/eddy current loss).
When loaded on secondary, Is becomes non-zero and generates a flux since current in a winding has a flux. This flux, per LL (law of Lenz) is of opposite polarity to the original. The core flux drops due to partial cancellation. The primary unloaded had a counter-emf nearly equal to source emf, the difference appearing across the primary winding impedance. Loaded, the counter-emf drops, so that the primary winding impedance has a voltage equal to the source emf minus a reduced cemf, resulting in larger primary current Ip. This Ip has a field and brings the flux back close to its original value so that secondary voltage is almost equal to the unloaded value.
Ampere's law AL, states that balance is achieved when the amp-turns of the primary balance that of the secondary, i.e. NpIp = NsIs. The transformer is self regulating, errors incurred since windings have resistance and leakage inductance. So the flux and voltages do not quite reach their original unloaded value, but come within a couple percent.
Claude