Waveform of Classic Electromagnetic Induction

[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.

 

[Delta2]

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.

The coil doesn't need to know anything as you said, it just obeys the laws of physics and mathematics. The laws of physics tell us that the induced EMF is the first derivative (with respect to time) of the magnetic flux. The laws of mathematics tell us that this first derivative become zero when the function, that is the magnetic flux attains a maximum (or a minimum). It doesn't need to remain constant to maximum just to attain a maximum at an instant in time. The laws of math also tell us that this function of magnetic flux attains a maximum when the angle between the magnet axis and the coil axis becomes zero.

 

[b.shahvir]

The coil doesn't need to know anything as you said, it just obeys the laws of physics and mathematics. The laws of physics tell us that the induced EMF is the first derivative (with respect to time) of the magnetic flux. The laws of mathematics tell us that this first derivative become zero when the function, that is the magnetic flux attains a maximum (or a minimum). It doesn't need to remain constant to maximum just to attain a maximum at an instant in time. The laws of math also tell us that this function of magnetic flux attains a maximum when the angle between the magnet axis and the coil axis becomes zero.

Your response is still mathematical and not analytical.

 

[Delta2]

Your response is still mathematical and not analytical.

Well kind of agreed to that, my answer is based on a mathematical understanding of the physical laws, rather than on a qualitative /intuitive understanding of the physical laws.

 

[b.shahvir]

Well kind of agreed to that, my answer is based on a mathematical understanding of the physical laws, rather than on a qualitative /intuitive understanding of the physical laws.

Kindly note, my intention is not to deny any physical or mathematical laws. I am just attempting to make an analytical approach to the subject.
My interpretation is that it does not matter to the coil if the flux is at maximum or minimum value at that instant. It only responds to changes in magnetic field strength. If the field strength does not change at that instant, the induced emf will be 0. This occurs when the pole tips are perfectly aligned with axis of the coil and the field strength is uniform near the pole tips. The maximum value of the field at that instant could be any non zero number.

 

[Tom.G]

I now have a slow motion video in .WMV format showing magnet position & waveform together. However, PF does not accept that format and I can't find any "accepted files" list.

Anyone have a fix or any clues?

Thanks,
Tom

 

[sophiecentaur]

Anyone have a fix or any clues?

Post the movie elsewhere and give a link in your PF post. YouTube works.

 

[alan123hk]

A qualitative /intuitive approach is always good but sometimes it leads us to the wrong conclusions and such is the case here

I very much agree with this. A slight negligence or lack of careful thinking due to laziness makes it easy to draw wrong conclusions based on intuitive analysis. I have made this mistake before. Intuition leads me to believe that when the poles are to the sides, and equidistant from the coil, the rate of change of magnetic flux should be zero, but this is not the case.

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

Fortunately, Charles Link's excellent analysis post #107 quickly pointed out this misunderstanding.

Tom's experiment result

 

[b.shahvir]

I very much agree with this. A slight negligence or lack of careful thinking due to laziness makes it easy to draw wrong conclusions based on intuitive analysis. I have made this mistake before. Intuition leads me to believe that when the poles are to the sides, and equidistant from the coil, the rate of change of magnetic flux should be zero, but this is not the case. Fortunately, the excellent analysis of post #107 quickly pointed out this misunderstanding.

View attachment 284412

Thanks for the graphical representation. It's awesome. Now anxiously awaiting Tom's video.
Also one thing evident from the flux graph is that the induced emf is 0 when magnetic field strength is uniform at the peaks albeit for a very short period of time. Of course these are the magnetic pole tips.

 

[b.shahvir]

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

Can I generate a perfect sinewave if I use a cylindrical dipole magnet as rotor? The experimental results with such an arrangement will be quite interesting.

 

[Paul Colby]

Can I generate a perfect sinewave if I use a cylindrical dipole magnet as rotor? The experimental results with such an arrangement will be quite interesting.

Yes. If the magnet is completely immersed in a uniform magnetic field while rotating. By a uniform magnetic field, I refer to one that is generated by, for example, a Helmholtz coil when the coil is energized by a constant current. In this case, the generated EMF by a spinning magnet is exactly a sinusoid. The generated EMF is related to the volume integral of a constant B field dotted with the magnetization. The only time dependence comes from the direction of the magnetization, which is a pure sinusoid in time.

[edit] Here I'm using the reciprocity theorem. Kind of advanced for a B-level thread. The reciprocity theorem showed up in post 49. Post 73 drops a few bread crumbs. One needs the time-harmonic Maxwell equations along with volume integration by parts, so the answer takes some math to see.