I have been doing some experiments on changing the medium contained inside a loop of wire from air to iron cores, and seeing the relationship between the potential difference established and the number of iron cores inserted inside the loop of wire. When I plotted the graph, the more iron cores I insert inside the loop of wire, the greater the voltage that was established in the circuit. Essentially I set it up like a transformer, and feed the primary coils with initial input voltage and see how the output voltage change in the secondary coils as I fill the transformer with iron cores instead of air.
My experiment Set up : I have no image but if I were to explain it, I have a long 30cm hollow rectangular cardboard, and coils wrapped around each end as primary and secondary coils. Then start the experiment by giving it initial input voltage, and slowly filling the hollow rectangular cardboard with iron cores.
But here is the problem, I expected some kind of linear relationship but when I graphed the voltage output (y a-xis), against the number of iron cores inserted (x - axis). However there seems to be a square root relationship. Now this is confusing to me because within my knowledge of physics and the mathematical equations, I cannot seem to explain this square root relationship.
Does anyone have an explanation for this square root relationship I am observing in my experiment?
(EDIT: Basically my question is why is there a square root relationship between the output voltage in secondary coils when graphed against the number of iron cores I used when I fill the transformer set up with iron cores instead of air (increase in magnetic permeability). Is there a mathematical relationship, or is it just my experimental error?)