The short answer is, “Yes.”
The longer answer exemplifies one of the lovely things about physics: its internal unity, and the fact that a few basic principles manifest in a plethora of circumstances. And one of the typical shortcomings of our textbooks (and by extension our lectures).
For me, this was one of the attractions of the subject when I was a young student … if one understood a few basic principles, and one had reasonably good mathematical technique, one could go far in understanding nature, at least in simple situations. But ay, there’s the rub: Physics is simple, but subtle. Even in the simple situations that physics is concerned with, deep and careful thought is often required to arrive at simple explanations, simple understandings, simple results.
Back to Lenz’s law. The textbook we’re currently using in the course I’m teaching states the law as follows (page 823):
There is an induced current in a closed, conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in the flux.
There follows several pages of very clear explanations and examples, including helpful diagrams.
The textbook misses an opportunity (as does every other textbook on my shelf) to make an important connection: Lenz’s law is just a version of Newton’s third law applied to a particular kind of situation; that is, a situation where a changing magnetic flux induces a current in a loop of wire.
Some of the books I consulted make the point that if Lenz’s law predicted the opposite orientation of induced current, then perpetual-motion machines would be possible, which would violate the principle of conservation of energy. Good. But going further to make the connection between Lenz’s law and Newton’s third law of motion would be better.
This is the purpose of teaching, which includes writing textbooks. All the information is already out there in cyberspace, readily available to anyone with an internet connection. Yet if the availability of information were all that were needed for good education, then everyone would be a genius by now. But, as Jacques Barzun stated, we think with ideas, not with information.
But this is what is largely missing in cyberspace: thinking tools; and making connections is one of the most important thinking tools. The giant textbooks we use are full of technical details, full of drill … we need more guidance for students in how to think.