Faraday's law of induction is not true
Michael 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.
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.
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.
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.
P.S. Consider also 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?
In relation to this please read also this answer on Quora: Is it possible to increase the current of a power source via an induced current
and the post on this forum: Inducing electric current in a wire by moving magnetic field
How does the induced current in a rotating loop look like?
Consider the following experiment:
A straight conductor is moving vertically exactly towards the middle of a magnet (figure a). No current is induced in this conductor.
In the second variant the conductor is shifted 1 millimeter to the right and is moving again vertically towards the magnet (figure b). 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.
Consider now this experiment:
A straight conductor is moving vertically exactly in the middle between two identical magnets as in the figure (a) above. 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 its 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 the 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 happens the reverse with respect to that of the figure (b).
Please look now at the figure below.
A straight conductor is rotating uniformly counter-clockwise in a homogeneous magnetic field according to the figure (what is meant by “homogeneous field”, please read Is the Flemings left hand rule valid/.) The rear end of the conductor (which is farther from us) is connected to the positive terminal of an oscilloscope, the front end to the negative. What will the graph of the induced current (/voltage) look like?
Please look at the picture below:
There are two crossed lines in it, which I have called “dead lines”. Whenever the conductor moves through one of those lines, there is no current induced in it. Therefore I called them “dead lines”. But in reality these dead lines are dead planes. The horizontal line I call the main middle plane.
Which plane is the vertical line? It can be any vertical plane which goes through the central point between the magnets. But which one out of the infinite number of them? That depends on the direction of the conductor. Let’s say that the rotating conductor is exactly in the North-South direction. In that case the vertical plane is also in that direction.
So, when the conductor is rotating in a homogeneous magnetic field as in the picture above, the induced current will be zero in the four points marked with the Roman numbers (graph below).
When a rectangular loop is rotating in a homogeneous magnetic field (figure below), then we have in fact only a second identical conductor which rotates diametrally to the first, because only these two sides of the loop play a role in the current induction (marked with “L” in the figure below). Since the current in the second conductor has the contrary direction, the induced current in the loop will be twice as strong (recall that it is a loop.) The graph above is valid also for this loop, only I have to draw the wave twice as high.