Waveform of Classic Electromagnetic Induction

[alan123hk]

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.

 

[Charles Link]

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.

 

[alan123hk]

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.

 

[Charles Link]

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. :)

 

[b.shahvir]

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

 

[Charles Link]

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.

 

[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.

 

[Charles Link]

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.

 

[alan123hk]

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

 

[b.shahvir]

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]

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.

 

[b.shahvir]

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]

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.

 

[b.shahvir]

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]

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]

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.

 

[b.shahvir]

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.

 

[b.shahvir]

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]

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.

 

[hutchphd]

Please justify your claim in detail. Or rescind it You made it.

 

[Charles Link]

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

The transformer, like an ac generator, also works according to Faraday's law $\mathcal{E}=-\frac{d \Phi}{dt}$.

Here we are trying to explain the ac generator, and your experiment with a rotating pole magnet and a coil makes for a simple home-made generator. In many cases, the coil, (instead of the magnet), is rotated in what is ideally a uniform (homogeneous) magnetic field. That can generate a very good sinusoid, because then we have the flux through the coil $\Phi=\Phi_o \cos(\omega t)$.

The rotating pole magnet version makes for a good laboratory demonstration, but because of the distorted sinusoids, as well as the very incomplete flux coupling, that geometry is generally not used in commercial electrical generators.

See https://www.physicsforums.com/threads/i-dont-understand-transformers-how-to-apply-them.1002399/
Transformers are a little more complicated than Faraday's law, but are also a good subject to study. The current balance properties, see post 12 of the "link", are very important.

For the transformer, normally an iron core is used. If I'm not mistaken, in general an electrical generator does not use an iron core.

 

[b.shahvir]

There seems to be some confusion arising from misinterpretation of my posts and the experimental set up in this case. I am not denying faraday's laws, but the references being put forth about emf induced in coil due to homogeneous magnetic fields does not relate to the present case of rotating magnet.
A bar magnet does not emanate homogeneous magnetic fields except at very close proximity to the pole tips. This is the reason why the induced voltage drops to 0 whenever the pole axis are perfectly aligned with the axis of the coil. At this position the magnetic pole is perfectly facing the center of the coil and due to near perfect homogeneity of the magnetic field near the pole tips, the rate of change of flux is 0 (although the magnet is in motion).
The output waveforms are already uploaded by Tom in this thread and for all to see. I request you all to have a relook at Tom's experiment and analyse the output waveforms carefully to note the position of the bar magnet when the voltage drops to 0. Thanks.

 

[Charles Link]

When the axis of the magnet is aligned with the axis of the coil, the magnetic flux is at a maximum. It is not a matter of being homogeneous here. When the flux has a peak,(in absolute value), it is simple calculus to see that $\mathcal{E}=-\frac{d \Phi}{dt}=0$.

 

[b.shahvir]

When the axis of the magnet is aligned with the normal to the plane of the coil, the magnetic flux is at a maximum. It is not a matter of being homogeneous here. When the flux has a peak,(in absolute value), it is simple calculus to see that $\mathcal{E}=-\frac{d \Phi}{dt}=0$.

I have attempted to explain the same in practical context. Although the magnet is in motion, the induced emf is 0 as rate of change of flux linkage is 0 due to homogeneity of the magnetic field at that instant.

 

[Charles Link]

I have attempted to explain the same in practical context. Although the magnet is in motion, the induced emf is 0 as rate of change of flux linkage is 0 due to homogeneity of the magnetic field at that instant.

It can help considerably to have a thorough mathematics background when analyzing some of the scenarios that appear in these E&M problems. In this case $\Phi=\Phi(\theta)$ and the function $\Phi$ peaks on-axis. By the chain rule, $\frac{d \Phi}{dt}=(\frac{d \Phi}{d \theta})( \frac{d \theta}{dt})$. When a (well-behaved) function has a peak, its derivative is zero at that point. This does not require a uniform field. In this case, it is a very narrow peak, and not a broad peak, so the zero of the derivative is present for only an instant, instead of being more prolonged.

 

[alan123hk]

My personal opinion is that whether it is motional EMF, transformer EMF, non-homogeneous magnetic field or homogeneous magnetic field, the conditions for the induced EMF to be zero are based on Faraday's law, that is, the rate of change of the magnetic flux through the coil is zero.

As for whether the induced EMF is a pure sine wave and whether there are double hump shapes, it depends on the specific conditions of the system, such as whether the magnetic field is non-homogeneous or homogeneous, the position and angle of the relative movement of the coil and the magnet, etc.

 

[b.shahvir]

Consider an hypothetical case of a bar magnet emanating an homogeneous magnetic field in all directions around it upto infinity. This implies that the magnetic field strength around this magnet does not change with distance upto infinity.
Now consider faraday's simple magnet and coil experiment. I will consider the coil to be wound on a ferromagnetic core for greater effectiveness. Now place this bar magnet along the axis of the coil at a finite distance from the face of the coil. Now move the magnet towards the coil with constant velocity.
It will be observed that the change in magnetic field strength will be 0 (homogeneous field) although the magnet is in continuous motion. In other words, the rate of change of flux linking the coil be 0, hence the induced emf in the coil will also be 0.

 

[Delta2]

Consider an hypothetical case of a bar magnet emanating an homogeneous magnetic field in all directions around it upto infinity. This implies that the magnetic field strength around this magnet does not change with distance upto infinity.
Now consider faraday's simple magnet and coil experiment. I will consider the coil to be wound on a ferromagnetic core for greater effectiveness. Now place this bar magnet along the axis of the coil at a finite distance from the face of the coil. Now move the magnet towards the coil with constant velocity.
It will be observed that the change in magnetic field strength will be 0 (homogeneous field) although the magnet is in continuous motion. In other words, the rate of change of flux linking the coil be 0, hence the induced emf in the coil will also be 0.

Yes in this example the homogenity of the field is what causes the induced emf to be zero. However it is not the same as the rotating magnet. There the emf becomes zero because the flux comes to a maximum as @Charles Link very successfully said at post #129. The flux comes to a maximum because if we do the math we can see that the flux depends on the cosine of the angle between the magnet axis and the coil axis, and this cosine is at maximum(=1) when the angle becomes zero i.e magnet axis align to the coil axis.

 

[b.shahvir]

Yes in this example the homogenity of the field is what causes the induced emf to be zero. However it is not the same as the rotating magnet. There the emf becomes zero because the flux comes to a maximum as @Charles Link very successfully said at post #129. The flux comes to a maximum because if we do the math we can see that the flux depends on the cosine of the angle between the magnet axis and the coil axis, and this cosine is at maximum(=1) when the angle becomes zero i.e magnet axis align to the coil axis.

Mathematically yes, but my explanation was pertaining to physical concept. The coil does not know mathematics, the coil
is not living thing to know that when the flux is maximum I need to reduce my emf to 0. So why does the emf become 0? Because in that position there is no further change in magnet field strength due to uniformity of the field near the pole tips at that particular instant in time. So in the absence of change of flux wrt time, the emf induced in the coil is 0. This is in purely physical context.

 

[Delta2]

Mathematically yes, but my explanation was pertaining to physical concept. The coil does not know mathematics, the coil
is not living thing to know that when the flux is maximum I need to reduce my emf to 0. So why does the emf become 0? Because in that position there is no further change in magnet field strength due to uniformity of the field near the pole tips at that particular instant in time. So in the absence of change of flux wrt time, the emf induced in the coil is 0. This is in purely physical context.

The coil does not know that the field is uniform near the pole of the magnet either.

Anyway I think your intuition tells you that is because of the uniformity of the field and you insist on your intuition. However when we do the math we get a different explanation, between your intuition and the math i choose what math say. Sorry!

 

[b.shahvir]

The coil does not know that the field is uniform near the pole of the magnet either.

It does not need to. The coil is simply a sensor. When the magnetic field strength variation linking the coil is 0 at any particular instant in time, the emf induced in the coil will be 0. It's just obeying laws of physics.

I think your intuition tells you that is because of the uniformity of the field and you insist on your intuition. However when we do the math we get a different explanation, between your intuition and the math i choose what math say. Sorry!

There is no intuition as explained above. The mathematical and physical conclusions are the same without contention. I simply attempted to explain the above phenomenon through a physical perspective.

 

[b.shahvir]

There the emf becomes zero because the flux comes to a maximum as @Charles Link very successfully said at post #129. The flux comes to a maximum because if we do the math we can see that the flux depends on the cosine of the angle between the magnet axis and the coil axis, and this cosine is at maximum(=1) when the angle becomes zero i.e magnet axis align to the coil axis.

As a matter of fact, how does the coil know the flux has attained maximum value and will not change further? How will it sense it? I don't think it will resort to solving mathematical equations

 

[Delta2]

As a matter of fact, how does the coil know the flux has attained maximum value and will not change further? How will it sense it? I don't think it will resort to solving mathematical equations

It can be said that the coil solves mathematical equations, that's how analog computers used to work.
The laws of physics are better expressed in the language of mathematics. A qualitative /intuitive approach is always good but sometimes it leads us to the wrong conclusions and such is the case here.

 

[b.shahvir]

It can be said that the coil solves mathematical equations, that's how analog computers used to work.
The laws of physics are better expressed in the language of mathematics. A qualitative /intuitive approach is always good but sometimes it leads us to the wrong conclusions and such is the case here.

Ok I maybe wrong for the sake of argument, but please make me understand analytically how the coil knows that the magnetic field has attained maximum value and there will be no further change in its strength at that instant.