I have a few questions regarding general transformer workings, and a couple of questions regarding toroidal transformers as well. For ease of reading I've put them in bullet points: 1. The magnetic flux induced by the primary winding creates the voltage (and hence current) across the secondary winding, but this secondary winding produces a magnetic flux which opposes (and TOTALLY cancels) the magnetic flux which created it, as per Lenz's law. Is this correct? 2. Continuing on from this, I've heard that since the initial power source has to compensate for this loss of flux in order to drive the secondary circuit, it boosts the power accordingly. But then surely now you have a greater flux being transferred from the primary, which would mean a greater reverse flux from the secondary...ad infinitum? I know I'm missing something simple here, but I cannot see it. 3. How can you prove mathematically that the voltage across the secondary winding is opposite to the primary winding (i.e. the current flows in the opposite direction; polarity is reversed?). If you take any standard textbook transformer (typical square shaped ring with the windings on opposite sides), the positive terminals are at the same position at any given time, meaning the voltages are opposite. As an example see below. My guess is the following, if you take vectors into account; Since V1/N1 = - dΦ/dt and we take the direction of an upward flux to be negative, then a downward flux (on the other side of the transformer) will be dΦ/dt, ergo dΦ/dt = V2/N2. Since now we end up with - V1/N1 = V2/N2, since we cannot have "negative turns", the only other conclusion is that V1 and V2 just have opposite signs in order for that equation to hold. please correct me if I'm wrong. 4. In a toroidal transformer, the primary and secondary windings are essentially on top of each other (obviously insulated so no short circuit). When I drew up a cross section of how a toroidal transformer would work, I noticed that the directions of the magnetic flux of the primary and secondary windings were going in opposite directions (regardless of whether I looked at the inner or outer part of the transformer). Do these fields have no impact on the efficiency of the transformer? I would assume they simple cancel in the area (albeit very small area) between the primary and secondary windings? Please forgive any seemingly mundane and trivial misunderstandings but I've never tackled these issues outside of high school. Thanks in advance for any help provided.