[Mitko Gorgiev (OP)]

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.

In almost every textbook on electromagnetism where the Faraday’s law of induction is discussed, there is an example of a usually rectangular wire loop which rotates in a magnetic field (drawing below).

wire loop.JPG (9.01 kB . 245x200 - viewed 10486 times)

What type of current is induced in this loop? Direct current, alternating current, or maybe, no current?

Consider 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.
We can imagine that inside this wire there is a propeller or there are many propellers in a row. When we 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 we 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 we cannot turn the propeller from above. Exactly the same picture we have with the magnet and the wire.


wire propeller.JPG (10.88 kB . 400x221 - viewed 10411 times)

After we have lowered the magnet down and have produced a current in one direction, then we can move it back upward. In that case we produce a current in the contrary direction, just as we will produce an air-current in the contrary direction if we turn the propeller from down up.

In producing the current in the rectangular loop, only the two shorter sides of the loop play a role. These relevant sides are marked with “L” in the drawing above. Their length is of no importance at all; the loop could be also a square.
Let’s look at the drawing below.

cross sections.JPG (20.05 kB . 413x321 - viewed 10521 times)

The loop in the drawing rotates counter-clockwise. When the right side of the loop moves up, then it is the same as if the upper and the lower magnet move down and the side is still. The induced current thereby flows away from us.

At the same time the left side of the loop moves down. The induced current in that side flows also away from us. Without knowing the right hand rule, we can conclude that the current in both sides flows in the same direction (this means: either towards or away from us) in the following way:
If the right side is moving up, then the current is flowing in one of the two possible directions; if the same side is moving down, then the current is flowing in the contrary direction (please recall on the experiment with the bundle). The reverse applies for the left side of the loop. So, when one side of the loop is moving up and the opposite side, of course, down, then the current in both sides is either towards us or away from us. But since it is a loop, these two currents cancel each other out. We have here something similar to the circuit below, where two identical batteries are connected as shown:

batteries.JPG (4.24 kB . 200x150 - viewed 10392 times)

No current can flow through this circuit.

The induced current in one of the relevant sides is a variable direct current (graph below).


graph1.JPG (8.17 kB . 504x150 - viewed 10362 times)

When one side is nearest to one of the magnets, then the current in that side is zero; when it is in the middle between the magnets, then the current in it is maximal. But since the same applies also to the other side, then for the whole loop we get the graph below:


graph2.JPG (17.72 kB . 504x321 - viewed 10467 times)

The resultant current is zero.

I have posted this answer as a further explanation to my assertion that the Faraday’s law of induction is not true. I explain it in detail in "Is Faraday's law of induction true?" https://www.thenakedscientists.com/forum/index.php?topic=78334.0

P.S. It is a well known experiment that when we move a magnet in or out of a solenoid, a current is produced in it. Instead of moving the magnet, we can move the solenoid towards or away from the magnet.
Let’s imagine that the solenoid has a shape of a square. Look at the picture below:

cross sections1.JPG (16.15 kB . 413x255 - viewed 16524 times)

The square loop is moving up toward the magnet. Since both sides are moving upward, the current in the right side is away from us, while the current in the left side is toward us. However, if the right side is moving up and the left down (as in the example of the rotating loop), then in both little circles in the drawing above I have to draw the letter x.

[Bored chemist]

Your diagram, cross sections.jpg, shows why the voltage falls to zero twice per revolution.

However, generators are known to work. So your assertion that the resultant current is always zero is obviously wrong.

[Hayseed]

It's regular current.

[Origin]

It's regular current

That's pretty funny... Thanks for the chuckle.

[Mitko Gorgiev (OP)]

Your diagram, cross sections.jpg, shows why the voltage falls to zero twice per revolution.

However, generators are known to work. So your assertion that the resultant current is always zero is obviously wrong.

Your comment shows that you haven't understood anything from what was written.

[Bored chemist]

Your comment shows that you haven't understood anything from what was written.

Well, I'm really quite clever, so what does your observation imply about your communication skills?

Work on them a bit, then come back.

[Mitko Gorgiev (OP)]

However, generators are known to work. So your assertion that the resultant current is always zero is obviously wrong.

However, you have admitted that there is an error in the explanation of the working principle of synchronous generators and motors.
https://www.thenakedscientists.com/forum/index.php?topic=78334.msg594180#msg594180

Well, I'm really quite clever ...

The others should judge how clever you are.

[Bored chemist]

However, you have admitted that there is an error in the explanation of the working principle of synchronous generators and motors.

No.
I said there's a poorly drawn diagram of it in a textbook.

The actual explanation is the physics, not a picture.

The others should judge how clever you are.

They will judge us both.

You claim

The resultant current is zero.

And, since generators actually produce current, you are wrong.
I don't need to be very clever to point that out.

[Mitko Gorgiev (OP)]

Well, I'm really quite clever ...

Can you solve this physics task? Since you are quite clever, it must be a piece of cake for you.

A single conductor is rotating uniformly in a magnetic field as in the figure below. Can you fill the coordinate system on the right with the waveform of the induced current in the conductor? Please pay attention to the four moments marked with Roman numbers.

Faraday law_1.jpg (20.86 kB . 580x340 - viewed 13839 times)

[Bored chemist]

I'm clever enough to say that it's impossible to answer.
When you say the induced current, do you mean the induced voltage?

Also, what sort of magnetic field did you imagine?
Are those magnets in the diagram cylinders or cuboid?

[hamdani yusuf]

A single conductor is rotating uniformly in a magnetic field as in the figure below. Can you fill the coordinate system on the right with the waveform of the induced current in the conductor? Please pay attention to the four moments marked with Roman numbers.

Using right hand rule, the current should be 0 at point II and IV. Maximum at point I (pointing out of screen). Minimum at point III (into the screen).

[hamdani yusuf]

P.S. It is a well known experiment that when we move a magnet in or out of a solenoid, a current is produced in it. Instead of moving the magnet, we can move the solenoid towards or away from the magnet.
Let’s imagine that the solenoid has a shape of a square. Look at the picture below:



The square loop is moving up toward the magnet. Since both sides are moving upward, the current in the right side is away from us, while the current in the left side is toward us. However, if the right side is moving up and the left down (as in the example of the rotating loop), then in both little circles in the drawing above I have to draw the letter x.

You should notice that the magnetic field working on the left conductor is pointing to down left while on the right conductor it's pointing down right. It's this magnetic field difference which makes difference in electromotive forces generated in either sides of the conductor when it's moving linearly.

[Mitko Gorgiev (OP)]

A single conductor is rotating uniformly in a magnetic field as in the figure below. Can you fill the coordinate system on the right with the waveform of the induced current in the conductor? Please pay attention to the four moments marked with Roman numbers.

Using right hand rule, the current should be 0 at point II and IV. Maximum at point I (pointing out of screen). Minimum at point III (into the screen).

No, Hamdani. You are very, very wrong. Would you try again?

[Bored chemist]

A single conductor is rotating uniformly in a magnetic field as in the figure below. Can you fill the coordinate system on the right with the waveform of the induced current in the conductor? Please pay attention to the four moments marked with Roman numbers.

Using right hand rule, the current should be 0 at point II and IV. Maximum at point I (pointing out of screen). Minimum at point III (into the screen).

No, Hamdani. You are very, very wrong. Would you try again?

Well, two of us say he's right and you are the only one saying he's wrong.

[Bored chemist]

I have sketched the lines of force onto the picture.
A voltage is induced when the wire cuts through the lines of force.
No voltage is induced when the wire moves along the lines.

fielded.png (80.72 kB . 832x508 - viewed 10697 times)

[Bored chemist]

At II and IV the motion is along the lines, so no voltage is induced.
At I and III the movement of the wire cuts directly across the lines and the voltage is a maximum.

So, Mitko Gorgiev, would you like to explain why you think everybody in the world is wrong, and you are right?

[Mitko Gorgiev (OP)]

So, Mitko Gorgiev, would you like to explain why you think everybody in the world is wrong, and you are right?

Do you believe that I do this out of fun - going against the whole world? No, I don't have fun at all. I innerly suffer because of that. But I am deeply convinced that the truth is on my side and I do this solely for the sake of the truth.
......

I have to make a small correction in the things said in my OP, but the essence remains the same.
The waveform of the induced current (it doesn't matter whether I say "induced current" or "induced voltage", since both have the same waveform) in the single rotating conductor will look approximately like this (I say "approximately" because it won't be an ideal half sine function at all):

Faraday law_2.jpg (36.9 kB . 560x340 - viewed 6314 times)

I will soon explain in details what this graph means.

[Bored chemist]

(it doesn't matter whether I say "induced current" or "induced voltage", since both have the same waveform)

Please stop posting dross like that. It's true in a single idealised case where the load is a pure resistor.
In the real world, it's wrong.

Do you believe that I do this out of fun - going against the whole world?

No, I think you do it out of conceit.

But I am deeply convinced that the truth is on my side and I do this solely for the sake of the truth.

And once again
If you are right and everybody else is wrong, how come nobody has noticed?

I will soon explain in details what this graph means.

Don't bother; It's wrong, for the reasons I gave earlier.

[Mitko Gorgiev (OP)]

Consider the following experiment: a straight conductor is moving vertically exactly towards the middle of a magnet. No current is induced in this conductor (figure a).
In the second variant (figure b) the conductor is shifted 1 millimeter to the right and is moving again vertically towards the magnet. A current is induced in it which flows away from us.
In the third variant (figure c) the conductor is shifted 1 mm to the left and is moving vertically towards the magnet again. A current is induced in it which flows towards us.

Faraday law_3.jpg (14.69 kB . 432x390 - viewed 6539 times)

Consider now this experiment: a straight conductor is moving vertically exactly in the middle between two identical magnets as in the figure (a) below:

Faraday law_4.jpg (8.27 kB . 370x400 - viewed 6538 times)

No current is induced in this conductor.
In the figure (b) the conductor is shifted 1 millimeter to the right and is moving again vertically from the lower to the upper magnet. A current is induced in this conductor. But during its movement upwards, the induced current changes the direction. To the dashed line (which is exactly in the middle between the magnets) the induced current flows towards us. When the conductor is exactly in the middle, the current drops to zero. Then, above the dashed line, begins a current flow in opposite direction.
In the figure (c) the conductor is shifted 1 millimeter to the left and is moving again vertically from the lower to the upper magnet. A current is induced in it, but here the reverse happens with respect to that of the figure (b).

Let’s now say that a closed wire loop is moving vertically between the two magnets.

Faraday law_5.jpg (12.88 kB . 285x368 - viewed 10880 times)

Through this loop will flow a current, but to the dashed line clockwise, above the dashed line counter-clockwise.
Now the question arises: how come a current is induced in the loop, when there is no change in the magnetic flux during the movement of the loop?
Moreover, why does the induced current change the direction at the dashed line in the middle?
How can these things be explained from the contemporary electromagnetic theory?

I will further elaborate this subject.

[hamdani yusuf]

Through this loop will flow a current, but to the dashed line clockwise, above the dashed line counter-clockwise.
Now the question arises: how come a current is induced in the loop, when there is no change in the magnetic flux during the movement of the loop?
Moreover, why does the induced current change the direction at the dashed line in the middle?
How can these things be explained from the contemporary electromagnetic theory?

There is indeed change in the magnetic flux during the movement of the loop. BC has drawn the magnetic field between those magnets.

From the picture above, magnetic flux is least dense halfway between the magnets, hence a loop moving upward from bottom to top will experience high - low - high flux density. The electromotive force is proportional to the flux rate of change, which is initially negative, then zero for a moment where it's in the middle, then positive when closer to the upper magnet.