Waveform of Classic Electromagnetic Induction Experiment 1

[shahvir]

Hi guys,

Can someone please provide graphical representation (waveform) of emf induced in coil due to a bar magnet spinning perpendicular to axis of coil as illustrated in attachment.

Thanks,
SB

 

[electricpete]

I'll pass. I misunderstood the question (thought rotation was simply spinning the magnet about its axis which is same as axis of coil) in which case the answer was simple and I tried to provide a "clever" clue would take zero time to sketch. Not clever anymore though.

Now I see the pivot point is in the center of the magnet. I think you provided plenty of information.
The waveform could be sketched in various levels of exactness. Noting that quantitative dimensional information is missing that would be required for exact solution, I'm guessing the teacher would be happy with a very simple sketch.


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[shahvir]

As per graphical results from the swinging magnet experiment in the attached pdf, the voltage peak occurs when the magnet pole is just near the midpoint of the coil (for both cases of poles approaching and leaving the coil) as the rate of change of flux is maximum at that point.

So a sine wave will be induced in coil but it's pattern would alternate between double positive and negative peaks in progression as the N & S poles alternately sweep across the plane of the coil.
For eg., negative voltage peak as N pole approaches the plane of coil, then 0V at center of coil when flux is maximum and again positive voltage peak as N pole leaves the plane of coil. Same pattern will repeat but with inverted voltage peaks when S pole sweeps along. I just wanted to confirm whether my graphical assumption was correct. In my opinion this may be closest simulation of my rotating magnet case.

 

[electricpete]

ok, you've put some thought into it. I'll tell you my opinion the teacher would be happy with a sinusoid.
The trickier part of the sinusoid would be to synchronize it with the magnet.
Max rate of change of flux (max voltage magnitude) occurs where magnet is vertical, min rate of change of flux (min voltage magnitude) occurs where magnet is aligned to the axis.
If you want to get the polarity correct, remember positive-direction flux loop flows from N->S outside a magnet, and remember the direction of induced voltage/current would be in a direction that tends to oppose the change in flux.... to figure that out you also have to remember your handrule taking note of the direction that the coil is wound.

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[shahvir]

'Max rate of change of flux (max voltage magnitude) occurs where magnet is vertical, min rate of change of flux (min voltage magnitude) occurs where magnet is aligned to the axis'.

But as per the results of the swinging magnet experiment, the max. voltage peak occurs when pole is at a position near to the center of the coil and not when the magnet has swung away from the face of the coil. Wouldn't the same waveform pattern mimic for the rotating magnet case too?

 

[electricpete]

> But as per the results of the swinging magnet experiment, the max. voltage peak occurs when pole is at a position near to the center of the coil and not when the magnet has swung away from the face of the coil. Wouldn't the same waveform pattern mimic for the rotating magnet case too?

I didn't delve into the swinging magnet but if it's like a pendululm than it is not moving at constant velocity. That may be the difference.

In your assigned problem there's not reason to assume anything other than a constant rotational velocity.
So it gives a sinusoidal flux (as a reasonable approximation assuming air coil... depends on level of detail required) .... max flux when the magnet is horizontal and zero flux when the magnet is vertical
But you're interested in rate of change of flux. Max rate of change of a sinusoid occurs at the zero and min rate of change occurs at the peak of the sinusoid.
So max induced voltage when magnet is vertical, min when horizontal.

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[electricpete]

I had a different interpretation - I took center of rotation as center of magnet since there is a dot there that could be a pivot.

Note op stated "bar magnet spinning perpendicular to axis of coil", which is admittedly vague, doesn't exactly match either of our interpretations (magnet is not spinning in the plane perpendicular to the axis).

I can't answer with 100% certainty what was intended. I give the teacher an F on this question.

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[IRstuff]

bar magnet SPIN axis perpendicular to axis of coil

There, do you feel better ;-)

TTFN (ta ta for now)
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[shahvir]

Note op stated "bar magnet spinning perpendicular to axis of coil", which is admittedly vague, doesn't exactly match either of our interpretations (magnet is not spinning in the plane perpendicular to the axis).

The illustration at the beginning of the thread clearly indicates the position of the magnet wrt the coil. I don't think there should be any doubt in interpretation of the apparatus after that.

 

[electricpete]

> The illustration at the beginning of the thread clearly indicates the position of the magnet wrt the coil. I don't think there should be any doubt in interpretation of the apparatus after that.

We see where it is, we're just not 100% certain where it's going.
I interpreted it as pivoting about the centerpoint shown on the magnet.
Bill interpreted it as pivoting around the centerpoint of the handle held by the mysterious hand above the magnet. ("Assuming that the center of rotation is the fist...")

Bill asked if his interpretation is correct.
Since it's your grade on the line (and you might have a better feel for what types of problems the prof is likely to throw at you), we'll go with your answer. So what is your answer?
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[shahvir]

I interpreted it as pivoting about the centerpoint shown on the magnet.

Your interpretation is correct. It's just like a primitive hand driven permanent magnet generator.

From the swinging magnet experiment representation I presume the sinusoids will reverse direction for each pole generating double positive and negative peaks at regular intervals in time. I don't know if it's correct to assume as such.

 

[electricpete]

Thanks for the feedback.

I had in mind that one complete rotation of the magnet would give one complete cycle of the sinusoid which is the simplest possible answer to the question. It's not necessarily the most accurate, but again you don't have a lot of dimensional data to work with to sketch a more quantitatively correct solution which makes me think the prof was looking for the simple solution.

Certainly if there was an iron core in the winding, the sinusoid could be quite a bit more distorted due to gap geometry as the magnet swings by the end of the core, but the figure suggests an air core winding to me.

If we want to compare it to the pendulum waveform, remember again the non-constant velocity of the pendulum motion, that tends to create higher velocities at the bottom and squeeze all the rate-of-change action into a narrow band of time where the magnet is near max velocity near the bottom of the swing. To convert it to my model of a rotating magnet, you'd have to stretch your pendulum waveform way out in time so that each of the two lobes in your pendulum figure would overlap with one of the lobes from an adjacent swing of an opposite-polarity magnet (same polarity voltage)... resulting in one sinusoidal cycle of voltage per magnet revolution.

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(2B)+(2B)' ?

 

[shahvir]

To convert it to my model of a rotating magnet, you'd have to stretch your pendulum waveform way out in time so that each of the two lobes in your pendulum figure would overlap with one of the lobes from an adjacent swing of an opposite-polarity magnet (same polarity voltage)... resulting in one sinusoidal cycle of voltage per magnet revolution.

I thought so too, but this phenomenon may apply to speed emfs (dynamo) rather than rate of change of flux emfs because when the magnet is completely vertical (90deg) wrt coil plane, the flux linking the coil would be 0. Even rate of change of flux will require presence of some finite flux element to induce emf in coil. Hence this confusion.

 

[shahvir]

There will be 0 emf state whenever the poles align with the axis of coil ( as rate of change of flux linkage is 0) and also 0 emf state when the magnet poles are 90 deg wrt axis of the coil (again rate of change of flux linkage is 0). So the result should be
0 +V 0 -V 0 and 0 -V 0 +V 0 per cycle for N and S poles respectively.
I wonder what the waveform will look like.

 

[IRstuff]

It'll look similar to the example C in the linked article

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[shahvir]

It'll look similar to the example C in the linked article

Yes but will it be exactly applicable to the rotating magnet case? If so this arrangement may not be suitable for designing practical alternators, just saying.

 

[srini1785]

I guess some math is in order.

EMF = -Nd(phi)/dt

Where:

d(phi)/dt = rate of change in flux = BAcos(theta)= BAcos(wt)
w=rotational speed in rad/sec
B= Magnet strength
A= Cross sectional area
N= Number of turns

Just assume some values for B,w ,A and N and get values for EMF (Yaxis) for times (X axis) and plot. Its no big guess work that it would be cosine graph.

PS : its been some time since i did some high school math so not sure if it should be cosine or sine.

 

[electricpete]

> when the magnet is completely vertical (90deg) wrt coil plane, the flux linking the coil would be 0. Even rate of change of flux will require presence of some finite flux element to induce emf in coil.

I disagree. The flux is passing through zero but its derivative is not 0 (It's derivative is maximum magnitude). When a ainusoid passes through 0, its derivative (slope) is maximum.


> There will be 0 emf state whenever the poles align with the axis of coil ( as rate of change of flux linkage is 0)

Yes.

> and also 0 emf state when the magnet poles are 90 deg wrt axis of the coil (again rate of change of flux linkage is 0).

I disagree. When the magnet poles are at 90 degrees, the flux is 0 but the rate of change of flux is maximum.
Similar to how at t=0, the sin function is 0 but it's derivative (the cos function) is max.

> So the result should be

... a sinusoid whose period is the time for one full rotation of the magnet.

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(2B)+(2B)' ?

 

[shahvir]

I disagree. When the magnet poles are at 90 degrees, the flux is 0 but the rate of change of flux is maximum.
Similar to how at t=0, the sin function is 0 but it's derivative is max.

> So the result should be

... a sinusoid whose period is the time for one full rotation of the magnet.

Ok then why do graphical results of the swinging magnet experiment differ from the rotating magnet case? The waveform of the experiment clearly indicates that the sinusoid completes one cycle when only one pole links the coil. Another inverted sinusoid cycle will follow when the other pole links the coil, so on and so forth respectively. That means 2 sinusoid cycles for one complete rotation.

 

[electricpete]

> Ok then why do graphical results of the swinging magnet experiment differ from the rotating magnet case? The waveform of the experiment clearly indicates that the sinusoid completes one cycle when only one pole links the coil. Another inverted sinusoid cycle will follow when the other pole links the coil, so on and so forth respectively. That means 2 sinusoid cycles for one complete rotation.

I already addressed this in my last paragraph 3 Jun 21 19:34 where I said "each of the two lobes in your pendulum figure would overlap with one of the lobes from an adjacent swing of an opposite-polarity magnet (same polarity voltage)... resulting in one sinusoidal cycle of voltage per magnet revolution"

Let me see if an example makes it clearer:
Let's say we swing a pole by 6 times (N, S, N, S, N, S), then I claim there are three cycles of sinusoidal voltage

Here are the individual swings and their voltage polarities:
N pole swings by creating 2 voltage pulses (+,-)
S pole swings by creating 2 voltage pulses (-,+) (note the sequence of +/- reverses when you switch the pole polarity)
N pole swings by creating 2 voltage pulses (+,-)
S pole swings by creating 2 voltage pulses (-,+)
N pole swings by creating 2 voltage pulses (+,-)
S pole swings by creating 2 voltage pulses (-,+)


Let's list all those voltage pulses next to each other in time:
(+,-) (-,+) (+,-) (-,+) (+,-) (-,+)

You'll notice that if I compare the 2nd element in one parentheses to the first element in the next parentheses, they are the same polarity. (decreasing flux from north pole as it leaves induces same polarity voltage as increasing flux from south pole as it approaches... and decreasing flux from south pole induces same polarity voltage as increasing flux from north pole)

Let's re-arrange the parentheses to emphasize what I said in previous paragraph
+ [-, -] [+, +] [-, -] [+, +] [-, -] +

Now remember what I said about overlapping. Everything I showed in square brackets represents two pulses of the same polarity that overlap in time. They form one pulse whose magnitude is the sum of the two pulses. Rewrite it as follows
+ [-] [+] [-] [+] [-] +

The five square bracketed items in the middle of the pattern would correspond to 2.5 cycles of a sin wave.
How do we treat the + at the beginning and the + at the end? IF we combined them with the additional adjacent + voltage pulse before and after from additional adjacent pole swings before and after this series of six, THEN they would each contribute a half cycle. BUT since we're not including those adjacent pulses from pole swings outside our series of six, we have to call each of those + voltage pulses at the beginning end of our pattern a quarter cycle. So we have 2.5 cycles in the middle, quarter cycle at each end, it adds up to three cycles like I said.

Sorry for so many words. This overlapping is an easy concept, but tough to explain without pictures.

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(2B)+(2B)' ?