# The results of my magnetic flux data from voltage recorded

For my electrical engineering senior design I created an experiment to test magnetic flux (more voltage) through a receiving coil.
There is a large sending coil with A.C. voltage and a small receiving coil with an oscilloscope measuring voltage_pp. Its wireless power.

I ran three tests. One with the two coils, and two experiments with different metallic materials in the center of the receiving lens. Sort of a wireless transformer. I have results. I found online that flux has a 1/r^2 relationship. My results show a 1/x at almost the entire range of distances. When the two lenses are close I think mutual inductance comes in and stops the constant increase of voltage measured. If I plot voltage against 1/distance I definitely get a straight line. This would mean a 1/x relationship right? But online everywhere its 1/x^2. Also my large sending coil has a big radius which I'm wondering if that matters. If i take my slope from the straight line its voltage/(1/x) = voltage*x which is a weber? Or flux? I was really happy to see the slope is units of magnetic flux but I'm unsure. (its cm so not exactly weber but i can change to meters later)

Big takeaway is why my results are 1/x and am interpreting the results of my slope correctly? I'm all on my own on this experiment, my group mates have done nothing lol and my prof has admitted to not knowing what wireless power transfer is about. Any help would be appreciated. (I have a capacitor on my receiving coil so the voltage induced can have zero impedance by sending the ac voltage at its LC resonant frequency. The tested material would change resonance but everything was in the range of 190kHz - 210kHz.)

• I think you have a significant detuning effect. These are definitely near field measurements and detuning of the transmit coil by a tuned receive coil can make a nonsense of measurements. At the frequencies you are using far-field will be 100s of metres away. Try the experiment without using tuning capacitors and please also explain what you mean by lenses. – Andy aka Oct 18 '20 at 17:06
• "lens" A and B were how I labeled the two metallic materials i put inside my receiving coil. What do you mean by detuning? All three tests had some resonance because its an LC circuit. The metallic "lens" would lower the resonance frequency but not by much. Makes sense because f is proportional to 1/sqrt(L) and the metal inside increases L. Every time I ran the tests at each lenses exact resonant frequency. – Chris Bolig Oct 18 '20 at 17:15
• As you bring the small tuned coil close to the big tuned coil you will get some detuning. – Andy aka Oct 18 '20 at 17:18
• yes actually I left off data on that graph. I stop plotting at 7.5 centimeters because after that it wasn't a steady increase of voltage. – Chris Bolig Oct 18 '20 at 17:22

There may be some detuning effects, but another effect is that you have a large driving loop. The magnetic field along the axis of a circular loop of wire is actually proportional to

$$B_z \sim \frac{1}{(z^2 + R^2)^{3/2}}$$

where z is the distance along the axis and R is the radius of the loop(reference).

This alone won't account for your entire observation, as it is still steeper than the $$\1/z\$$ dependence you are seeing, but it is probably part of the story of what is going on.

I actually figured it out, I wasn't giving the whole story. (also re-did experiment for cleaner measurements). I knew the equation for B(z) ,like you suggested, from the center of the loop. Here are my original plots. (So many plots because the point is to test voltage as a function of material inside the receiving coil)

I thought this decline in the increase of voltage (guess d^2/dx^2 < 0) was from mutual inductance. Like the field from the receiver effecting the original resonance. (Even labeled it on the original graph)

I plotted a y(x) = 1/((x^2 + const^2)^3/2) online and it looks like that graph. I took one of the data points and plotted its x axis as 1/((x^2 + 11^2)^3/2). The entire range was almost linear

Please ignore the title or units, and I took off x-axis uncertainties. The radius of my large coil was about 11cm and I'm not even sure how "centered" my receiving coil was. Not bad.

If you try the fit with r = 15cm

See how wrong it gets. I'm happy about this and thought I would share. I believe this shows this classic B as a function of a loop of wire holds.

• Thank you for following up and taking time to share your findings. It is nice to see the resolution. – rpm2718 Oct 25 '20 at 11:53