In the same way that increasing the speed of movement of a magnetic field through a coil of wire will increase the tension induced in the coil, if a magnetic field can be made to collapse more rapidly, this will induce a higher voltage. According to Faraday's Law, the greater the speed at which the magnetic field changes, the greater the induced electromagnetic field (EMF). Additionally, the more turns there are in the secondary coil, the greater the induced EMF. If we increase the turns of the secondary coil, the output voltage increases proportionally. To understand this concept better, imagine a straight piece of wire that is used to make a magnet.
When this wire is wrapped into coils, it rolls up so that the lines of magnetic force are parallel and point in the same direction. If the secondary coil has more turns than the primary coil, then the output voltage is greater than the input voltage. On the other hand, if the number of turns of the secondary coil is less than the number of turns of the primary coil, then the output voltage will be lower than the input voltage. In technical terms, each coil of wire increases the magnetic flux density (force) of the magnet. We discovered that the relationship between the induced EMF and the input voltage is equivalent to that between the turns of the secondary coil and those of the primary coil.
Iron is a magnetic material, so it guides and directs the magnetic field from one coil to another. As such, as voltage increases with more turns, current decreases due to resistance and inductance (the ability of a coil to generate a magnetic field in response to a current).However, if you wrap this cable around a core (let's say it has a straight solenoid magnet), you are reshaping and redirecting its field lines (in addition to concentrating them in a smaller size).
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