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

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).

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.

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.

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 left, right and who knows what hand’s rules (please see this answer on Quora Was Fleming’s left hand rule created to make physics students look stupid?) 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 to 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:

No current can flow through this circuit.

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

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:

The resultant current is zero.

Consider also the following: 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 we have to draw the letter x.