# Waveform of Classic Electromagnetic Induction

• B
Nope I dont agree with that, the two positive humps is when the north pole is approaching the coil and leaving the coil, and the third hump inbetween is when the north pole is aligned with the coil, thats what I think.
Similarly for the two negative humps and the south pole.

I would politely disagree. On careful analysis you will find the double humps(+ & - ) are actually formed when the poles reverse.

Let's say the the N pole is approaching the coil = 0 to +A
Next, the N pole is perfectly aligned with the axis of the coil = 0 state.
Again N pole is leaving the coil = 0 to -A
Next, the magnet is aligned perpendicular to axis of coil = 0 state
Next, the S pole is approaching the coil = 0 to -A (this is actually the 0 state between the double humps)
And the process continues as above....

hutchphd and Delta2
Delta2
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Next, the magnet is aligned perpendicular to axis of coil = 0 state
I disagree only with this, we dont get a 0 when this happens instead we get a positive local minimum (or a negative local maximum ).

hutchphd
I disagree only with this, we dont get a 0 when this happens instead we get a positive local minimum (or a negative local maximum ).

Why? Could it be due to magnet field geometry or stray induction in oscilloscope probes or due to instability of the string! What prevents the voltage from going to 0 especially when the waveform is not a sinusoid.

Is it an air coil or iron core coil? In my opinion the non zero state could be due to output current inductance in case of iron core coil.
Or maybe this is a current waveform. For proper voltage waveform you might require to drop it across a load resistance.

Delta2
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Is it an air coil or iron core coil? In my opinion the non zero state could be due to output current inductance in case of iron core coil.
Or maybe this is a current waveform. For proper voltage waveform you might require to drop it across a load resistance.
Could be due to the self inductance of the coil but I doubt it, i think its because of the magnet field geometry as you said.

alan123hk and b.shahvir
It seems that we all have a consistent view of the waveform.

Actually my prediction is ##~+A→0-A→0→-A→+A→0→+A##
But the result of the experiment is ##~+A→0-A→\text{local max}→-A→+A→\text{local min}→+A##

I am also confused about why the zero that should appear between the double hump becomes a local minimum/maximum.

I agree that this may be caused by the geometry of the magnetic field, or more specifically, it may be because the relative positions and/or angles of the rotating magnet and the coil are not very symmetrical.

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b.shahvir and Delta2
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The voltage is caused by the time derivative of the flux. When the poles are to the sides, and equidistant from the coil, the total flux is zero, but the derivative can be near maximum. This is where you observe the slight dip between the peaks, which occur just before and just after this position.

b.shahvir, vanhees71, alan123hk and 1 other person
The voltage is caused by the time derivative of the flux. When the poles are to the sides, and equidistant from the coil, the total flux is zero, but the derivative can be near maximum. This is where you observe the slight dip between the peaks, which occur just before and just after this position.

I totally agree with your excellent analysis. When the magnetic poles are on both sides and are equidistant from the coil, the effective magnetic flux through the coil is zero, but this is only a point on the time axis. More importantly, even at this point in time, the magnetic flux through the coil is still changing, so now I believe this is the real cause.

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This simple home-made ac electrical generator would really make for a good experiment for undergraduate physics and EE students to perform. The mathematics could be refined by computing, per post 72, the magnetic flux from the cylindrical magnet. (It should be a fairly routine thing to computer program the magnetic flux, and numerically compute the time derivatives, etc., to compare experimental with theoretical). Thank you @Tom.G for supplying us with some very good experimental data in post 92. :)

Tom.G, b.shahvir and Delta2
This simple home-made ac electrical generator would really make for a good experiment for undergraduate physics and EE students to perform. The mathematics could be refined by computing, per post 72, the magnetic flux from the cylindrical magnet. (It should be a fairly routine thing to computer program the magnetic flux, and numerically compute the time derivatives, etc., to compare experimental with theoretical). Thank you @Tom.G for supplying us with some very good experimental data in post 92. :)

As inferred from the experiment, we find that the output waveforms are quite unique and not a sinusoid. But sadly, theoretical representation (wherever I was able to observe) always indicate it as a sinusoid.
This gives an incorrect impression to the students that under all and any arrangement of faraday's EMI apparatus, the result will always be sinusoidal. Thanks to Tom, we can now clearly see the real picture. I once again am very grateful to Tom for this.

Tom.G
Is it an air coil or iron core coil?
Air.

Speculation here, could the dip between the double-humps be when the magnet axis is parallel to the coil axis?

It will be a few days before I have the opportunity to document the magnet position vs. waveform.

Cheers,
Tom

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Speculation here, could the dip between the double-humps be when the magnet axis is parallel to the coil axis?
See post 107. I believe it occurs when the two are perpendicular.

hutchphd, Delta2 and b.shahvir
Can this experiment be redone with a longer bar magnet? I believe in this case the interim state between 2 double humps would then drop to 0.

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The idea of an iron core (post 104) is an interesting one. I do think in that case the iron in the core might reach a state of saturation during much of the cycle. If that indeed is the case, the voltage would see a spike, followed by a lengthy duration near zero, and then a spike in the reverse direction, followed by a lengthy duration near zero. It would be interesting to see if this is indeed the case. If the core didn't saturate, it could result in a stronger signal. One additional experiment would be to move the magnet farther away, and see if the iron core would then be free of saturation.

Can this experiment be redone with a longer bar magnet? I believe in this case the interim state between 2 double humps would then drop to 0.
If the induced voltage of the coil becomes zero between the double humps, it will take some time for the magnetic flux through the coil to remain constant. If this happens, one of the sufficient conditions should be that the rotating magnet must produce concentric magnetic lines of force within a certain angle range. But is it possible for a magnet to produce such magnetic field lines of force?

https://en.wikipedia.org/wiki/Magnetic_dipole#/media/File:VFPt_dipoles_magnetic.svg

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Actually it's the other way round. I believe the length of the magnet will directly influence the magnetic field geometry and hence the output voltage waveform. Consider the long bar magnet aligned perpendicular to axis of coil (vertical). In this case, the voltage dip will be significant (might even drop to 0) as the flux lines are more flattened at this position indicating a very slow rate of change of flux.
If it were a short dipole or a one turn air coil, then the induced voltage would have been maximum at above position. This is because the flux lines would be semicircular and the rate of change of flux linkage will be maximum at this position producing a perfectly sinusoidal output waveform. I hope my interpretation is correct.

Delta2
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producing a perfectly sinusoidal output waveform
I think in order to get a perfectly sinusoidal voltage we need a homogeneous magnetic field rotating (or a coil rotating inside a homogeneous magnetic field). The field from any sort of dipole is not homogeneous. It can be almost homogeneous very near the poles but varies greatly when you move far away from the poles.

The two humps look like they are part of a sinusoidal curve, but they are formed when the poles are approaching the coil, so that the field there is almost homogeneous.

I think in order to get a perfectly sinusoidal voltage we need a homogeneous magnetic field rotating (or a coil rotating inside a homogeneous magnetic field). The field from any sort of dipole is not homogeneous. It can be almost homogeneous very near the poles but varies greatly when you move far away from the poles.

The two humps look like they are part of a sinusoidal curve, but they are formed when the poles are approaching the coil, so that the field there is almost homogeneous.

In my opinion, the rate of change of flux linkage will be minimum in homogeneous field so output voltage will be 0 near that position. The humps indicate maximum voltage level attained at a particular magnet position at that particular instant of time, but may not indicate the peak value of the entire output waveform. The peak value would depend upon the maximum rate of change of flux linkage at a particular instant in time where the field is non homogeneous.

Delta2
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In my opinion, the rate of change of flux linkage will be minimum in homogeneous field so output voltage will be 0 near that position.
If the homogeneous field is rotating then the rate of change is not minimum as you say , instead it follows a perfect sinusoidal curve. Check in google the principle of AC voltage generation.

If the homogeneous field is rotating then the rate of change is not minimum as you say , instead it follows a perfect sinusoidal curve. Check in google the principle of AC voltage generation.

The above principle applies to motional emfs (dynamically induced), not transformer emfs (rate of change of flux)

hutchphd
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The above principle applies to motional emfs (dynamically induced), not transformer emfs (rate of change of flux)

What are you talking about? This is extraordinarily incorrect. Please provide references.

Delta2
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The above principle applies to motional emfs (dynamically induced), not transformer emfs (rate of change of flux)
The principle is one: Faraday's law of induction. It can be used for motional emf and transformer emf.

The principle is one: Faraday's law of induction. It can be used for motional emf and transformer emf.

With reference to the present rotating magnet case, then why does output voltage become 0 when the magnetic poles are perfectly aligned with the axis of the coil?(horizontal position). The magnetic field in close proximity to the poles is homogeneous, hence rate of change of flux is 0 at this position. My context was related to the present case and not in general.

weirdoguy
What are you talking about? This is extraordinarily incorrect. Please provide references.

Please explain me relation of homogeneous magnetic fields with statically induced emfs (transformer principle)

Delta2
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The magnetic field in close proximity to the poles is homogeneous, hence rate of change of flux is 0 at this position
You got it wrong, because the magnetic field is homogeneous, it doesn't necessarily mean that the rate of change of flux is 0. Please check the principle of AC sinusoidal voltage generation. There you have a homogeneous magnetic field and a rotating coil.