The Naked Scientists
  • Login
  • Register
  • Podcasts
      • The Naked Scientists
      • eLife
      • Naked Genetics
      • Naked Astronomy
      • In short
      • Naked Neuroscience
      • Ask! The Naked Scientists
      • Question of the Week
      • Archive
      • Video
      • SUBSCRIBE to our Podcasts
  • Articles
      • Science News
      • Features
      • Interviews
      • Answers to Science Questions
  • Get Naked
      • Donate
      • Do an Experiment
      • Science Forum
      • Ask a Question
  • About
      • Meet the team
      • Our Sponsors
      • Site Map
      • Contact us

User menu

  • Login
  • Register
  • Home
  • Help
  • Search
  • Tags
  • Recent Topics
  • Login
  • Register
  1. Naked Science Forum
  2. On the Lighter Side
  3. New Theories
  4. Is Faraday's law of induction true?
« previous next »
  • Print
Pages: [1] 2 3 4   Go Down

Is Faraday's law of induction true?

  • 64 Replies
  • 40066 Views
  • 4 Tags

0 Members and 4 Guests are viewing this topic.

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Is Faraday's law of induction true?
« on: 21/12/2019 09:47:40 »
MODERATOR WARNING:
THIS POST AND OTHERS BY THE SAME POSTER APPEAR TO BE EDUCATIONAL IN NATURE, HOWEVER THEY CONTAIN SERIOUS ERRORS AND SHOULD NOT BE TAKEN AS SCIENTIFIC PRINCIPLES.


No, Faraday’s law of induction is actually not true.

One of the fundamental laws of electromagnetism is the “Faraday's law of induction”. This law states that the induced voltage in a wire loop is equal to the speed of change of the magnetic flux enclosed with the loop, or V=dΦ/dt. In the textbooks is often given an example of a loop in the shape of a rectangle which rotates in a magnetic field.


* rotating loop.JPG (9.01 kB . 245x194 - viewed 7703 times)

What is meant by “the speed of change of the magnetic flux enclosed with the loop”?

To explain this, we will make a comparison. If we hold a ring in front of our eyes as if we want to see through it, then it has a shape of a circle. If we turn it 90°, we only see a line. In every other intermediate position of the ring, we see an ellipse. In the first position, the ring has the maximum area in front of our eyes; in the second, the minimum, i.e., zero. If the ring starts to rotate about its axis starting from the second position (0) and has turned 180°, then the area we see in the course of this rotation can be represented with a sine curve of half a period.

Similarly, when the wire loop is in the vertical position (image above), then the magnetic flux is zero, and when the wire loop is in the horizontal position, then the flux is maximal. This flux changes according to a sine function, too. So, when the flux is maximal, then the speed of its change is minimal, more precisely, zero, because the slope of the sine curve in this point is zero. But when the flux is minimal, then the speed of its change is maximal, because the slope of the curve in this point is maximal.

So, from the Faraday's law of induction it follows that when the wire loop is in vertical position, then the induced current in the loop is maximal; and when it is in horizontal position, then the current in the loop is zero.

I claim that just the opposite is true, because it is not relevant the speed of change of the magnetic flux through the loop, but the speed of the wire towards the magnet or away from it. In producing the current in the rectangular loop, only the two shorter sides of the loop play a role. When these sides are nearest the magnet, then their speed of moving towards or moving away from the magnet is zero, thus the current is also zero.

For better understanding, let’s take a look at this picture. The projection of the circling dot on the vertical axis behaves like a pendulum. When the projection dot is at the top or at the bottom of the vertical axis, its speed is zero. And when it is in the middle, its speed is maximal. The same concept applies also to the two mentioned sides of the wire loop.


* circling dot.JPG (7.29 kB . 437x186 - viewed 7737 times)

I claim that the concept of the contemporary physics called “magnetic flux through a surface” is an absolute misconception, something that is not founded in the reality. What real is and what relevant is to this case are two things: first, the strength of the magnetic field, and second, the speed of the conductor towards the magnet or away from it, that is, the component of this speed which is in line with the magnetic lines of force, not the component perpendicular to them, as it follows from the Faraday’s law of induction.

As a consequence of this misconception follows another, and that is the misexplanation of the working principle of synchronous generators and motors. Let’s look at this picture from a textbook called “Elektronik 1” from the following authors: Helmut Röder, Heinz Ruckriegel, Willi Schleer, Dieter Schnell, Dietmar Schmid, Werner Zieß, Heinz Häberle. The picture refers to synchronous motor, but it can also refer to synchronous generator. On the picture we see a magnet, three coils and three sine curves: black, blue and red. The black sine curve corresponds to the current of the black coil. From the picture we see that in the first position of the rotating magnet the current in the black coil is zero; in the second position, the current in that coil is maximal.


* GENERATOR MOTOR MISCONCEPTION.JPG (55.39 kB . 602x440 - viewed 7923 times)

Just the opposite is actually true (this means: in the first position the current in the black coil is maximal; in the second, it is zero). And with this new explanation the torque from the coils upon the rotating magnet is the same at every moment of time, as it should be for its smooth rotation.

The other concept is contradictory, because the torque is not the same at every moment. Let’s take a look at the second position of the magnet when it is in line with the black coil (the current at this moment is at maximum)(the magnet rotates counter-clockwise). Until this moment the coil has attracted the white pole; then the pole goes to the left side of the coil; the coil still has the current in the same direction, which means that it still attracts the pole and thus acts against the direction of rotation. At the same moment (i.e., when the magnet is in line with the black coil) the blue and the red coil have equal currents in the same direction and both act on the opposite pole of the magnet. Thereby both exercise an attractive force. It follows that the red coil attracts the lower pole of the magnet in the direction of rotation and the blue coil attracts it against the direction of rotation. We see that on two places, both up and down, contradictory effects take place. When the upper pole of the magnet has passed the black coil a little bit, then of the three coils only the effect of the red one on the magnet will be in the direction of rotation, making the whole assembly impossible.

When the pole of the rotating magnet is moving towards the coil, then the coil attracts it. When the pole is exactly in line with the coil, then the current comes to zero, the magnetic field, too. Then a current flow begins in the contrary direction, the magnetic field of the coil is reversed and it begins to repel the pole of the magnet. This applies to a motor. The reverse applies to a generator.

I have great esteem for Michael Faraday and have searched his work to find where he has defined this law, but unsuccessfully. If someone can cite where it is, I will be very grateful to him/her.

P.S. Consider this very well-known experiment: we move a magnet in and out of a solenoid. Instead of moving the magnet, we can move the solenoid.
Is the wire of the solenoid moving perpendicular to the magnetic lines of force, or is it moving in line with them?

P.P.S. Consider also the following experiment: from a lacquered copper wire we cut off twenty to thirty pieces of about 10 cm. From them we form a bundle of parallel wires and connect the two ends with one more wire each. The other ends of these two wires are connected to a sensitive analog ammeter. We hold the bundle horizontally and move quickly a strong and broad magnet downwards on its left side. The pointer of the instrument will make a deflection to one side. If we now move the magnet quickly downwards on the right side of the bundle, the instrument will make a deflection to the opposite side. The magnetic flux that we have produced in the wire is now in the opposite direction to the one in the first case, which is why the deflection is in the opposite direction. The motion of the magnet produces current even if we only approach it to the bundle from one side without lowering it below the bundle. In this case the current is somewhat weaker. But if we now move the magnet down to the middle of the bundle, the instrument won’t show any current, because the left and the right halve of the magnet act on opposite sides of the bundle, canceling each other out.
We can do the experiment with only a single wire instead of a bundle, as long as we have a very strong magnet and a very sensitive ammeter.
You can imagine that inside this wire there is a propeller or there are many propellers in a row. When you turn a propeller manually from the left side, then it is turning in one direction and it is blowing on one side (plus), but it is suctioning on the other side (minus). When you turn the propeller from the right side, then it is turning in the contrary direction and the air current is in the opposite direction. But you cannot turn the propeller from above. Exactly the same picture we have with the magnet and the wire.


* propeller analogy.JPG (10.88 kB . 400x221 - viewed 7847 times)

P.P.S. The shape of the magnetic forces in and in the vicinity of the poles of a, let’s say, cylindrical magnet is twisted, similar to a stranded wire.


* stranded wire.JPG (6.64 kB . 450x200 - viewed 8174 times)

When we lower the magnet on one side of a metal wire, then we can imagine something similar to two helical gears at angle of 90 degrees. The twisted field of the permanent magnet is the one gear; the induced magnetic field in the wire, which is also around the wire and is also spiral-shaped, is the other gear.
The twisted field of the permanent magnet is static when the magnet is not moving. When the magnet is moving, then its field is moving together with the magnet. This moving magnetic field we can call a magnetic wind. When we lower the magnet on one side of a metal wire, then this magnetic wind generates another magnetic wind in the wire, whose effect is tangible also around it. This opposes to the first, just as a mechanical gear would offer a resistance to another gear by which is moved. And just as the resistance of the second gear is greater when the load on it greater, so it is the resistance of the induced magnetic field to the moving magnetic field when the electrical load in the circuit is greater.

When we generate electric current in a solenoid by moving a magnet in and out of it, then we have a device very similar to the mechanical “push and spin” devices, which can be found in kids toys, ashtrays etc.
« Last Edit: 01/03/2020 15:34:48 by Colin2B »
Logged
 



Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #1 on: 21/12/2019 11:54:33 »
TLDR
Please explain how things actually work.
All the designs are based on the idea that the physics is correct.
If the physics is wrong, how does the design work?
Logged
Please disregard all previous signatures.
 

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Re: Is Faraday's law of induction true?
« Reply #2 on: 21/12/2019 13:07:50 »
The design works because of a lot of practical work of many people through many generations, not because the physics is correct.
Logged
 

Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #3 on: 21/12/2019 14:15:28 »
Quote from: Mitko Gorgiev on 21/12/2019 13:07:50
The design works because of a lot of practical work of many people through many generations, not because the physics is correct.
You seem to have missed the point.
Faraday's law of induction is vital to a lot of design.
It feeds into Maxwell's equations so, if you were right it wouldn't just be all the designs for motors, generators that failed (and even then people would have noticed the discrepancy.)
The whole science of radio transmission wouldn't work.

I know I keep saying this but, you really should learn some science before trying to pick holes in it.
All you are currently doing is demonstration your own lack of understanding.
Logged
Please disregard all previous signatures.
 

Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #4 on: 21/12/2019 14:25:19 »
Also, you have fundamentally misunderstood the physics/ maths.

As you say the "induced voltage in a wire loop is equal to the speed of change of the magnetic flux enclosed with the loop, or V=dΦ/dt. "
And, from your picture of the circling dot it's clear that near the top and bottom of the circle, the rate of change of the enclosed field is zero, and that's when the induced voltage is zero.
At the top and bottom of the circle the dot is travelling more or less horizontally- which means the wire moves along the magnetic field, rather than cutting through it.
That's why the induced voltage there is zero.

I think you have mistaken the field for the rate of change of the field.

At any rate, you are clearly wrong. Such a fundamental issue in physics wold have been spotted a long time ago.
Logged
Please disregard all previous signatures.
 



Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #5 on: 21/12/2019 14:26:20 »
Quote from: Mitko Gorgiev on 21/12/2019 09:47:40
I have great esteem for Michael Faraday and have searched his work to find where he has defined this law, but unsuccessfully. If someone can cite where it is, I will be very grateful to him/her.
Can you read Latin?
Logged
Please disregard all previous signatures.
 

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Re: Is Faraday's law of induction true?
« Reply #6 on: 22/12/2019 12:18:06 »
Quote from: Bored chemist on 21/12/2019 14:25:19
And, from your picture of the circling dot it's clear that near the top and bottom of the circle, the rate of change of the enclosed field is zero, and that's when the induced voltage is zero.
Your head is full of envy, so you cannot read and think clearly.
The example of the circling dot actually applies to my explanation and has nothing to do at all with the rate of change of the flux enclosed with the loop.
The example of the ring which rotates in front of our eyes has rather to do with the standard explanation, i.e., with the Faraday’s law. When the loop in the presented image in my original post is in vertical position, then the flux through it is zero, but the speed of change at that moment is maximal. So, the current is also allegedly maximal. But I assert that in that moment the current is zero, because the speed of moving towards or away from the magnet of the relevant side of the loop’s wire comes to zero.

The rotating loop doesn’t produce an alternating current, but a variable direct current (drawing below). I haven’t made this experiment, but I can say that for sure. Actually I doubt that many people have made it, because the experimental setup is not easy to prepare.


* VARIABLE DC.JPG (7.59 kB . 509x170 - viewed 7372 times)

Many people comment on the part with the rotating loop (I have posted this text also in other forums), but nobody comments on the part related to the synchronous generator and motor, that is, on the part related to the image from the German textbook. Why? I know why. Because the misconception is here strikingly obvious.

I can’t read Latin, but if you have a citation where Faraday has defined this law, just post it. I will find someone to translate it to me.
Logged
 

Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #7 on: 22/12/2019 14:51:33 »
Quote from: Mitko Gorgiev on 22/12/2019 12:18:06
Your head is full of envy,
It is fairly clear that I think you are a fool.
Even if I was wrong  about that, I'd have no cause to envy you.
Quote from: Mitko Gorgiev on 22/12/2019 12:18:06
The rotating loop doesn’t produce an alternating current,
This would be news to the people who make generators.
Quote from: Mitko Gorgiev on 22/12/2019 12:18:06
I haven’t made this experiment, but I can say that for sure. Actually I doubt that many people have made it, because the experimental setup is not easy to prepare.
It's a high school experiment.
You have got the wrong answer.

As I said, you should try learning.
Logged
Please disregard all previous signatures.
 

Offline hamdani yusuf

  • Naked Science Forum GOD!
  • *******
  • 11794
  • Activity:
    91%
  • Thanked: 285 times
Re: Is Faraday's law of induction true?
« Reply #8 on: 26/12/2019 10:50:39 »
Quote from: Bored chemist on 21/12/2019 14:26:20
Quote from: Mitko Gorgiev on 21/12/2019 09:47:40
I have great esteem for Michael Faraday and have searched his work to find where he has defined this law, but unsuccessfully. If someone can cite where it is, I will be very grateful to him/her.
Can you read Latin?
Most of Michael Faraday's books were written in English. In his time, Latin was no longer the main language for scientific publications.
https://www.goodreads.com/author/list/112273.Michael_Faraday
https://en.wikipedia.org/wiki/Michael_Faraday#Bibliography
Logged
Unexpected results come from false assumptions.
 



Offline evan_au

  • Global Moderator
  • Naked Science Forum GOD!
  • ********
  • 11033
  • Activity:
    8%
  • Thanked: 1486 times
Re: Is Faraday's law of induction true?
« Reply #9 on: 26/12/2019 21:06:54 »
Quote from: OP
their speed of moving towards or moving away from the magnet is zero, thus the current is also zero.
This presumes a purely resistive load.

If the load has an inductive or capacitive component, then current will be flowing when the wire is not moving relative to the magnet.
Logged
 

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Re: Is Faraday's law of induction true?
« Reply #10 on: 30/12/2019 07:37:53 »
Quote from: hamdani yusuf on 26/12/2019 10:50:39
Most of Michael Faraday's books were written in English. In his time, Latin was no longer the main language for scientific publications.
Dear Hamdani,
I am pretty sure that Faraday didn't define the law which bears his name neither in Latin nor in English. The Bored Chemist is just bluffing.
« Last Edit: 30/12/2019 07:41:01 by Mitko Gorgiev »
Logged
 

Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #11 on: 31/12/2019 12:20:12 »
Quote from: Mitko Gorgiev on 30/12/2019 07:37:53
The Bored Chemist is just bluffing.
Guess again
Much of the correspondence on science at that time wasn't in English.
I'm sure we are all waiting for you to answer my question
If it's "wrong", how come it works?
Logged
Please disregard all previous signatures.
 

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Re: Is Faraday's law of induction true?
« Reply #12 on: 10/01/2020 18:21:53 »
Quote from: Bored chemist on 31/12/2019 12:20:12
Much of the correspondence on science at that time wasn't in English.
It is completely irrelevant whether it was in English or Latin. You have promised a quotation from Faraday in Latin where he has defined the law of induction. But you are just a bluffer. You don't have it.
Quote from: Bored chemist on 31/12/2019 12:20:12
I'm sure we are all waiting for you to answer my question
If it's "wrong", how come it works?
What is it that works? The machines work, surely, the generators and motors. But do you believe that Ferrari, Dolivo-Dobrovolsky, Tesla and many others during their work on the construction of the generators and motors had in their heads the Faraday's law? It's ridiculous. They didn't give a toss about the theory. They wanted to make something that works and left the theory to the theorists. They were surely no theorists.
Logged
 



Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #13 on: 10/01/2020 18:32:12 »
Quote from: Mitko Gorgiev on 10/01/2020 18:21:53
You have promised a quotation from Faraday in Latin
No I did not.
I was warning you that any original documentation from that period might not be much use.
Quote from: Mitko Gorgiev on 10/01/2020 18:21:53
What is it that works?
Your computer.
The fibre optics used in the internet.

Essentially you are asking the wrong question.
You should be asking "What doesn't work?"
Because, if you were right the answer would be "everything more complicated than a steam engine".
Do you think people are still using  generators designed by Tesla?
Don't you understand that design has moved on since then and now relies on the theories that you are saying (without any evidence) are false?

Are you actually able to answer my question?


Quote from: Bored chemist on 21/12/2019 11:54:33
Please explain how things actually work.
All the designs are based on the idea that the physics is correct.
If the physics is wrong, how does the design work?


Quote from: Bored chemist on 21/12/2019 14:15:28
Faraday's law of induction is vital to a lot of design.
It feeds into Maxwell's equations so, if you were right it wouldn't just be all the designs for motors, generators that failed (and even then people would have noticed the discrepancy.)
The whole science of radio transmission wouldn't work.
Logged
Please disregard all previous signatures.
 

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Re: Is Faraday's law of induction true?
« Reply #14 on: 20/02/2020 23:56:14 »
Quote from: Bored chemist on 10/01/2020 18:32:12
Faraday's law of induction is vital to a lot of design.
It feeds into Maxwell's equations so, if you were right it wouldn't just be all the designs for motors, generators that failed (and even then people would have noticed the discrepancy.)

I haven't seen a comment of yours on the topic "Is the explanation of the working principle of synchronous generator and motor true?" and it is there already ten days.

What's the matter?

https://www.thenakedscientists.com/forum/index.php?topic=78617.0
Logged
 

Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #15 on: 21/02/2020 09:53:40 »
Quote from: Mitko Gorgiev on 20/02/2020 23:56:14
Quote from: Bored chemist on 10/01/2020 18:32:12
Faraday's law of induction is vital to a lot of design.
It feeds into Maxwell's equations so, if you were right it wouldn't just be all the designs for motors, generators that failed (and even then people would have noticed the discrepancy.)

I haven't seen a comment of yours on the topic "Is the explanation of the working principle of synchronous generator and motor true?" and it is there already ten days.

What's the matter?

https://www.thenakedscientists.com/forum/index.php?topic=78617.0
If you posted less balderdash I mightn't miss bits of it.
I have not seen your post yet.
What odds would you give me that I can't point out that it's wrong?
(You might want to re-read this thread first)
Logged
Please disregard all previous signatures.
 

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Re: Is Faraday's law of induction true?
« Reply #16 on: 21/02/2020 12:35:22 »
Quote from: Bored chemist on 21/02/2020 09:53:40
What odds would you give me that I can't point out that it's wrong?
Since you are the smartest man in the world, the odds are zero.
I am all ear.
Logged
 



Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #17 on: 21/02/2020 12:39:41 »
It didn't   take me long to find a bit that was wrong.
Quote from: Mitko Gorgiev on 12/02/2020 10:46:32
I have explained that in this thread "Is Faraday's law of induction true?" https://www.thenakedscientists.com/forum/index.php?
No you haven't.

By the way, is that whole post just dedicated to the fact that there's a mistake in the drawing?

« Last Edit: 21/02/2020 19:25:28 by Bored chemist »
Logged
Please disregard all previous signatures.
 

Offline Mitko Gorgiev (OP)

  • Sr. Member
  • ****
  • 165
  • Activity:
    0%
  • Thanked: 2 times
Re: Is Faraday's law of induction true?
« Reply #18 on: 21/02/2020 18:38:21 »
Quote from: Bored chemist on 21/02/2020 12:39:41
It didn't   take me long to find a bit that was wrong.
Quote from: Mitko Gorgiev on 12/02/2020 10:46:32
I have explained that in this thread "Is Faraday's law of induction true?" https://www.thenakedscientists.com/forum/index.php?
By the way, is that whole post just dedicated to the fact that there's a mistake in the drawing?

No you haven't.
LOL, the smartest man in the world doesn't know what to say.

By the way, the error is not accidental. The same picture can be found in many textbooks.
Logged
 

Offline Bored chemist

  • Naked Science Forum GOD!
  • *******
  • 31101
  • Activity:
    13%
  • Thanked: 1291 times
Re: Is Faraday's law of induction true?
« Reply #19 on: 21/02/2020 19:24:36 »
Quote from: Mitko Gorgiev on 21/02/2020 18:38:21
the smartest man in the world doesn't know what to say.
I wouldn't know about  him.
But I knew what to say.
What I said was that you were wrong- because you are.
Logged
Please disregard all previous signatures.
 



  • Print
Pages: [1] 2 3 4   Go Up
« previous next »
Tags: electromagnetism  / induction  / faraday's law  / electric current 
 
There was an error while thanking
Thanking...
  • SMF 2.0.15 | SMF © 2017, Simple Machines
    Privacy Policy
    SMFAds for Free Forums
  • Naked Science Forum ©

Page created in 0.492 seconds with 73 queries.

  • Podcasts
  • Articles
  • Get Naked
  • About
  • Contact us
  • Advertise
  • Privacy Policy
  • Subscribe to newsletter
  • We love feedback

Follow us

cambridge_logo_footer.png

©The Naked Scientists® 2000–2017 | The Naked Scientists® and Naked Science® are registered trademarks created by Dr Chris Smith. Information presented on this website is the opinion of the individual contributors and does not reflect the general views of the administrators, editors, moderators, sponsors, Cambridge University or the public at large.