If an inductor has current flowing in only one direction, does the magnetic field still vary directions? My understanding is that in a standard AC inductor the magnetic field in the core changes direction as the current through the primary coil alternates. What if the current through the primary coil was pulsed on and off but in one direction only?
It is still an alternating current that produces a changing magnetic filed that induces voltage in the secondary coil, but what happens to the magnetic field in the core? Would the secondary coil induce a magnetic field in the core the opposite direction to the field originally induced by the primary coil? Would the core still experience an alternating magnetic field, even though the primary coil current flows in on direction only?
My understanding of Lenz’s law is still a little shaky, and I am trying to understand how Lenz’s law would apply in this particular scenario. I feel like the secondary coil would induce a magnetic field in the opposite direction to the one induced by the primary coil, but I am not sure. 
(I am also not sure if I have not used the most fitting terms to describe magnetic field “directions”, but I hope people understand what I am clumsily trying to say!)
 A: The current in the primary induces a proportional magnetic field.
Any current in the secondary also induces a proportional magnetic field.
The observed magnetic field is the sum of the two.
So your interrupted-DC primary driver will drive a magnetic field that goes B-0-B-0-B etc.  
That'll induce a voltage in the secondary (it doesn't induce a current!) that goes + and - at the transitions between B and 0, and between 0 and B.  Depending on what's connected to the secondary, there might be a current in the secondary:


*

*If the secondary is open-circuited, nothing happens, and the field is as above.

*If there's a resistor, a limited current will flow. That'll create some magnetic field while flowing, which will be opposed to the change in the field:  If the primary is going 0 to B, it'll be negative; if the primary is going B to 0, it'll be positive.  That's Lenz's law in action. It'll tend to round-off the sharp transitions in the field given by the sharp transitions in the primary current.


The details of that second case are tricky, both mathematically and in practice.  I.e. you can't really instantly change the primary current; the primary is an inductor, and an infinite rate-of-change requires infinite voltage.  
It's really much easier to consider the sine/cosine case of continuous change, hence that's what we try to teach first.
