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I'm studying Inductive current in high school. I learned the Faraday law, and that the voltage produced is equal to the delta of magnetic field flux over time. So, I was curious about this topic and conducted an experiment. I found an inductor (a simple coil) and connected it with a multimeter set up to the current readings (in mA).

Then I bought some neodynium magnets, and I measured (10 readings / test) what is the max current induced when I let one magnet fall into the coil. Then I measure the reading with 2 magnets, then 3, and so on.

I came up with this graph:

Graph

On the x-axis there is the number of magnets piled up, and on the y-axis there is the current produced in mA. So, apparently, an increase in magnets is increasing the current produced, up to a limit though. After 12-13 magnets the current diminished, fixing to a value of about 2 mA regardless of the number of magnets.

So my intuition was this, If I increase the number of magnets, it will also increase the total magnetic field, so it wil produce more current. Searching on the internet I found that piling up too many magnets will actually decrease the magnetic field after some times, due to materials imperfections and dimension and shape of magnets, so I think that my data is coherent to that (but if you have more materials and sources about this decrease in magnetic force strenght you will make me happy).

The problem is that, if I initially thought "Ok, magnetic field is increasing, current is increasing", then I was more skeptical. If i look at the formula, I don't actually understand mathematically why an Increase in magnetic strenght should result in a more intense voltage / current. It is the variation of flux over time that creates current, so I can't understand. Can someone please explain me mathematically why the increasing in strength of the magnetic field will cause an increase in induced current?

Thank you very much!

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the voltage produced is equal to the delta of magnetic field flux over time

Faraday's law says induced EMF (not voltage) is proportional to rate of change of magnetic flux. Voltage depends on other things, such as whether the circuit is open or closed, and in the latter case on effective resistance of the inductor.

If the circuit is open, voltage has the same value as EMF, so your statement is correct then. But if it is closed, the EMF induces current through the inductor and if the latter has large effective resistance $R$, magnitude of voltage on it will be lower than magnitude of EMF by $|RI|$.

If you have a circuit with just a few coils and no core inside, then self-induction can be neglected and the induced EMF depends just on the rate of change of external magnetic field (due to magnets). The current that you try to measure depends on this induced EMF $\mathscr{E}$ and ohmic resistance of the whole circuit:

$$ I = \frac{\mathscr{E}}{R}. $$

Increasing the number of pill-shaped magnets in the column increases strength of magnetic field around the endpoints, but when the height of the column becomes larger than its diameter, this effect becomes smaller and smaller. This is because the added magnets are too far from the endpoint. In the limit of very long column, adding new magnets does nothing to strength of magnetic field near its end. That's why rate of change of magnetic field is not increasing much, and why induced EMF is not increasing very much.

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  • $\begingroup$ Thanks for the answer but math formulas are not displayed properly. $\endgroup$
    – TechMatt
    May 27, 2021 at 6:19
  • $\begingroup$ The formulas show correctly for me in Firefox, try reloading or other browser. $\endgroup$ May 28, 2021 at 13:49

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