Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.
Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).
What Notaros did was a math trick, very common in textbooks, but that unfortunately confuses KVLers. They think that if you model some circuit with an equivalent circuit, the components of that equivalent circuit will be found in the modeled circuit.
For instance, this is a very simplified model of a transistor for small signals at low frequencies.
KVLers think that if they open a transistor up they'll find a resistor connected in parallel with a voltage-controlled current source. Well, no. That's just a mathematical trick to help you solve the circuit. A lot of assumptions are implicit in this model. Some of them are in the model name. Signals must be small and frequencies, low, among other things (like, for example, ambient temperature, biasing, etc.)
Notaros modeling gives the same result if he decided to use Faraday's law, however there are a lot of assumptions that he doesn't mention, just as in the transistor model. One of them is that there's no real battery or generator in the path of the circuit.
KVLers can't understand that the battery they are looking for is not in the resistors or the wires. Their explanations always contradict each other. For example. When the loop with two dimensionally small resistors are connected with wires, they say that the voltage is generated in the wires, but not in the resistors. When we eliminate the wires, or when the wires are the resistors themselves, they say that itsy bitsy teeny tiny little batteries suddenly migrate inside the resistors.
What they don't tell you is when exactly these itsy bitsy teeny tiny little batteries migrate from the wires to the resistors. There's no theory to predict that. Search and you'll not find anywhere in the literature about electromagnetism.
Notaros, for example, contradicts the itsy bitsy teeny tiny little battery model, as he put two lumped generators in series with the resistors, although his loop is comprised of two resistive wires and nothing else.