What is assumed when this equation is used?
- All the magnetic flux produced by the primary couples to all other primary turns i.e. there is no leakage flux that can give rise to leakage inductance that gives rise to formula errors when there is a load or magnetization inductance (which there always will be).
- All the flux generated by the primary couples to all the turns on the secondary - this ensures that the voltage in the secondary is truly dependent on the turns ratio and the voltage ratio
However, meeting the above (and satisfying the equation) can be done theoretically with what we sometimes refer to as a non-ideal transformer. But only if that non-ideal transformer has zero leakage components (see below for the listings in the equivalent circuit). It can have magnetization current and, it can have core losses and the basic equation still works - this is because core losses and magnetization current are parallel to the ideal "inner transformer".
Transformer equivalent circuit showing leakages and magnetization inductance and losses: -
Picture from here
\$L_P\$ is the primary leakage inductance
\$R_P\$ is the primary copper loss
\$R_C\$ is the core losses due to eddy currents and hysteresis
\$L_M\$ is the magnetization inductance
\$L_S\$ is the secondary leakage inductance
\$R_S\$ is the secondary copper loss
If there is no loading on the secondary, \$R_S\$ and \$L_S\$ won't affect the output voltage. If the magnetization inductance and core losses (\$L_M\$ and \$R_C\$) are both very high impedances, then some leakage components on the primary (\$L_P\$ and \$R_P\$) can be tolerated without much detriment to the equation in question (providing there is still no load on the secondary).
Is transformer 1 an ideal transformer, or transformer 2
T1 might be an ideal transformer, T2 is not an ideal transformer
so in transformer 2, conceptually, less magnetic field lines go
through the secondary coil than the primary coil, therefore the
equation would not hold.