Transformers often require/use iron cores because they operate on magnetic forces, which are difficult to understand when sharing certain characteristics with good old "electricity" (ohms, volts, amperes, etc.). Let's try some simplified ways to get the overall idea. Start with a screwdriver - just a cylindrical coil. If we let the current flow through, a magnetic field (we call it the H field) is formed. The field depicted with the imagined field line flows up through the center of the coil, then disperses again after leaving the cylinder, then reassesses and re-enters the other end. You've seen the picture in the textbook. The magnetic field is strong and contained inside the cylinder (ID), while the magnetic field strength is weak outside (OD) because it diffuses in space. If the H magnetic field interacts with "anything" around the coil, whether it is vacuum, air or iron, it produces what we call a B magnetic induction field within the "material...