Clarification on This Transformer Statement
In a normal transformer there are two windings called primary and secondary. The primary refers to the driven winding i.e. the winding where AC power is fed. The secondary has a voltage induced and the turns ratio determines how big or small that secondary voltage is relative to the primary voltage. So, if the turns ratio is 1:1, and you fed the primary with 100 volts RMS, you would expect to see 100 volts RMS on the secondary.

In addition, the secondary voltage is in-phase with the primary voltage unless you swap the secondary wires to make it the inverse (180 degrees out of phase). Faraday's law ensures this.

If you then applied a 100 ohm load to the secondary, you would get 1 amp RMS flowing from the secondary and 1 amp RMS flowing into the primary. In other words power in equals power out (ideal transformer).

What actually makes a transformer "tick" is another current (called magnetization current). This is in addition to the 1 amp load current mentioned above. If you want to simply measure that magnetization current, you could remove the secondary load and use a current-shunt on the primary and what you would see is the magnetization current.

That magnetization current (for a sinewave applied voltage) lags the primary applied voltage by 90 degrees and is basically the current that would naturally flow into the primary should there be no secondary load (or the secondary winding were removed). It's the current flowing in an inductor and that inductance is the primary winding inductance.

So, there are two currents going into the primary when there is a secondary load: -


Magnetization current lagging by 90 degrees (always there) and
Primary referred secondary load current and, for a resistive load on the secondary, this current is in phase with the primary and secondary voltages.


The upshot of all of this (when you analyse a 1:1 transformer), is that the current entering the primary winding (due to the secondary load) is the same current as that leaving the secondary and flowing into the load. Given that the two windings are wound together, the net magnetic fields that they produce is big fat zero.

But there is still the good old magnetization current in the primary and that is unaffected by both secondary load current and primary referred secondary load current. And, importantly, it is that magnetization current that generates the secondary voltage so, any talk of load currents cancelling the magnetic field is largely from those who know little or believe they know more than they actually do..

Just consider this very simple example of applying a 1 volt step to the primary when the secondary has a load of 1 ohm: -



Picture from here.