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# Scientific article

**LEVER, CONDUCTOR IN A MAGNETIC FIELD, AND COVERED MAGNETIC FLUX**

The deepening global energy crisis as well as the effort to prevent as much as possible environmental pollution due to noxious gases from burning solid and liquid fuels and the potential danger for humanity that nuclear power stations pose urgently demand to search for and attempt to find new efficient alternative sources of energy. To everybody’s regret, however, present-day science is still looking for the final solution of this problem. While weighty research organizations worldwide invest enormous sums of money along these lines, my suggestion is, towards solving the energy problem, to take into consideration the result of a principal combination of the properties of the lever and those of a conductor placed inside a magnetic field, which combination explains the action of this latest of my inventions. Taken separately, we are quite familiar with those properties, but combining them in a certain manner, as elementary as that may seem from the point of view of mechanics, brings about the sought-for efficient result which has an important bearing on both science and progress. Notwithstanding that familiarity though, let us first, without going into too much detail, repeat the textbook essentials of those properties, and then cover, step by step, various principal positions and conjunctions between them, so that we may see what precisely the result that we have in mind is.

**Lever. **We know that the use of a lever yields force that utilizes a distance covered, while for it to be in equilibrium it is necessary that the forces acting upon it balance each other. This balance is achieved only when the product of one force and the respective arm of the lever is equal to the product of another and its other arm – fig.1.

**Electromagnetic force. **Fig.2 -When electric current flows along a conductor placed within a magnetic field, the interaction of this magnetic field and the electromagnetic field of the running current results in the conductor being influenced by an electromagnetic force F which moves it in a certain direction and accomplishes certain work. The overall expression of this force is F = BIℓ sinα, where F is the electromagnetic force, B is the magnetic induction, I is the amount of current, ℓ is the conductor’s length, and sin α is the angle between the conductor and the field’s magnetic lines. When this angle is 90^{o}, i. e. sin α =1, then this force has a maximum value.

**Electromagnetic** **induction.** Fig.3 shows a conductor of a certain length ℓ, placed in a magnetic field with B induction and which for a unit of time t moves at a V velocity over a certain distance from its initial position. This shift is marked with ∆X. The conductor’s length and the shift made, ℓ∆X, determine the area ∆S. During that shift, the conductor crosses a certain number of the magnetic lines of the field where it is, thus covering a magnetic flux, ∆Ф = В∆S. This process causes electrical propulsion tension (EPT) E=∆Ф/∆T. When an electric circuit using this conductor closes, induced electric current flows through the circuit, І = Е / R, where R is the whole circuit’s total resistance.

The direction of the induced current is always such that, in the conductor, an electromagnetic force is created which opposes the external cause of the shift, i. e. that force is directed in reverse of the movement, thus providing a resistance momentum. For this reason, the formula of electrical propulsion tension (EPT) already acquires a negative value, or Е = – ∆Ф/∆t. In physics the exercise of such a resistance momentum is acknowledged as ‘Lenz’s Rule.’

We shall begin elucidating the principle with Fig.4. For a lever whose short arm is loaded with several coils of conductor of equal size and weight so that F2 is the force of the 7g of their weight we’ll posit the exertion of force F1 on the long arm of the lever, which is equal to the force of 1g of weight that just one coil of conductor has, in order to shift the lever from position 1 to position 2 where it will be balanced. Upon exertion of this force of 1g, the lever shifts from position 1 to position 2. That meets the formula, F1ℓ1 = F2ℓ2 from Fig.1.

During that shift and balancing – Fig.4a – any one material point of the single coil of conductor on the lever’s long arm covers a longer distance S_{1 }than the distance S_{2 }covered by any one material point of the load on the lever’s short arm. It is apparent that the impact of the small force of 1g, exerted on the lever’s long arm, lifts the much bigger weight of 7g placed on its short arm. Briefly, using the lever results in the gain of force, which is compensated by a distance covered, S1 > S2, a

fact familiar from the textbook.

Using the lever with the coils of conductor we already looked at, we shall expound a few more configurations, uncoiling however the conductor and attaching it to the respective points of application parallel to its axis of rotation. Those conductors shall be posited as being influenced by magnetic fields with an equal magnetic induction and also perpendicular to the magnetic lines. Without at first considering the conductors’ weight factor, for now our main attention shall be directed at the magnetic flux ∆Ф covered by them. For a start, we shall fix and uncoil one conductor only at the points of application of both arms of the lever, parallel to its axis of rotation, which is mandatory – Fig.5.

As a second move, we shall shift this lever from the extreme upper position 1 of its long arm to its extreme lower position 2. Thus being shifted, each of the conductors, while crossing the field’s magnetic lines, shall cover a magnetic flux ∆Ф in accordance with its length and the distance it has covered. It is clear from the figure that the magnetic flux ∆Ф_{1}, covered by the conductor on the long arm, is bigger than the magnetic flux ∆Ф_{2}, covered by the conductor on the short arm, which is due both to the distances covered by the conductors and their lengths. The EPT induced in these conductors shall correspond to the magnetic fluxes covered, and if we decide to extract electric current from them during their movement, then the current from the long arm shall prove bigger than the current from the other conductor. Viewing that same lever and that same shift, to equalize the magnetic fluxes covered, ∆Ф_{1 }and ∆Ф_{2}, we can increase the length of the short arm’s conductor by what is needed, say by uncoiling another of those coiled conductors of Fig.4a. After that adjustment and the shift we are familiar with we see that the magnetic fluxes covered have now equal values, ∆Ф2 = ∆Ф1 – Fig.6. From the equation it follows that the amounts of current that can be extracted from these conductors shall be equal, too.

As not all conductors balancing the lever with the force of weight in Fig.4a have been uncoiled, we shall continue this operation and uncoil another of them. The maximum number that we are justified in uncoiling is the one that ensures the lever’s equilibrium. Each subsequent lengthening of the lever’s short arm beyond that in Fig.6 till the lever has been finally balanced by the forces of weight shall lead to the respective increase of the covered magnetic flux ∆Ф2, and as soon as the first lengthening is made the balance of covered magnetic fluxes will be destroyed. As a consequence, the EPT induced in it and the respective current will be increased as well. After the lengthening, we can see in Fig.7 that now ∆Ф2 > ∆Ф1.

From the above discussion of the lever and the successive transformations via the uncoiling of a different number of conductors it becomes apparent that, with one and the same shift and angular deflection that are being done simultaneously, in the individual cases we get different results in respect of the EPT induced in the conductors, which, as we see, is mostly due to their size. And if we view the conductors just as material points, no matter what their size and the magnetic fields’ influence are, the ratio of the distances covered by them, S_{1 }and S_{2}, always remains the same.

Fig.8 illustrates a state of the lever balanced by the forces of weight, which is done with those same conductors of Fig.4a, this time however with all the conductors uncoiled. From this point on, our interest shall be turned towards the conductors’ weight, too, as we compare them with the flowing currents’ values that correspond to them.

Making use of this equilibrium in Fig.8, let us now see what is going to happen when to the balanced state we add the influence of electromagnetic forces. To do it, we shall introduce, at the small conductor outlet in Fig.8a, an **I**d electric current with such a direction that, when flowing under the influence of the magnetic field, it shall generate a downward electromagnetic propellant force in the conductor, which will breach the existing balance and deflect the lever’s big arm towards its lowest position. That way, the small conductor will become propellant. Simultaneously, the short arm with the big conductor will move upwards and find itself in its highest position. If the flow of an Id electric current of a given power along the propellant conductor creates a propellant electromagnetic force **F**d whose value is equal to the force of weight 1g of that same conductor, i. e. Fd = 1g, then for the lever’s equilibrium to be restored it will be necessary to apply to its short arm once more either the force of weight of the big conductor, which is 7g, or else let flow along it a current of such power and direction that an electromagnetic propellant force be created, Fk, directed downwards and whose value corresponds to the weight of that same conductor, i. e. Fk = 7g. This current Ik, creating the electromagnetic propellant force Fk = 7g, we can call ‘balancing current’. Until the value of the balancing current Ik that feeds the big conductor is reached, it is but natural that the values corresponding to the weights of 1g, 2g, 3g, 4g, 5g, and 6g shall be traversed, and it is clear they cannot balance the lever. Only when the balancing current Ik = 7g is introduced the lever’s equilibrium is restored – Fig.8a.

If we have the lever in equilibrium secured by the electromagnetic forces Fd and Fk that are equal in value to the force of the weight of the conductors that balance the lever at both ends 1g and 7g, i. e. Fd =1g and Fk = 7g, it is clear that the ratio of the currents introduced, Id and Ik, shall be the same as the ratio of the forces of the weights. Having in mind this fact and the bigger covered magnetic flux ∆Ф2 from the big conductor that we acknowledged in Fig.7, when the free rotation of the lever around its axis is ensured, by feeding a propellant current Id to the propellant conductor, according to the law of electromagnetic induction EPT will be induced. Linking the conductor to an electric circuit, induced electric current will flow that we shall mark by It. In this way the big conductor will start to generate current. The flow of that current, as is well-known from Lenz’s Rule, will create a resistance momentum according to its value and it will strive to halt the action of the cause creating it, i. e. stop the rotation. The greater the current the generating conductor takes in, the greater the resistance momentum. The thing we stressed above regarding the rising value of the balancing current Ik that was let flow along the big conductor to create a propellant force Fk balancing the lever we now can partially repeat regarding the value of the induced current It. Till the value of the balancing induced current Ik and the respective balancing force are reached, taking into consideration the inevitable losses, it is only natural that the values of the current corresponding to 1g, 2g, 3g, 4g, and 5g are to be passed through which for obvious reasons cannot stop the rotation. Only when the value corresponding to the resistance momentum, say of 6g, is reached shall the movement be principally stopped. The value at which the movement stops and consequently the process of generation itself we shall call ‘critical value’. In respect of the acting and counteracting forces the mathematical precision of the equilibrium is absolute, but since there exist inevitable losses accompanying the process, in respect of the values of the current Ik and the current It is natural that there should be a difference between them.

It is logical to ask about the efficiency value of the generated current. On principle the flow of electric current starts at zero and, increasing, reaches a certain value. Since here we have a movement of the generating conductor as a consequence of feeding current to a propellant conductor, having also in mind the inevitable losses, the minimum value of the efficient generated current shall be a little over the value of the current Id feeding the propellant conductor. We shall call that current ‘initially efficient current’. If we have an initially efficient current, it follows we should also have a ‘closing efficient current’. We noted above that at reaching the current’s critical value, a value equal for instance to 6g, the movement will stop, which means that the maximum efficient value will be below the critical one, say one corresponding to a weight of 4g or 5g. Consequently, the generated current’s upper limit of efficiency shall be the value at which it is going to be several times the value of the propellant current Id, and at the same time the movement will be stable, sustained by that same propellant current, i. e. that will be the nominal current In. In other words, the value of the nominal generated current In will be several times greater than the value of the current Id that was used to generate it. Such a result is guaranteed by the very construction that contains the sufficient length of generating conductor placed inside a magnetic field as well as by the ratio of the distances of the separate conductors to the lever’s axis of rotation. It is essential to reiterate the fact that the processes of propelling and generation are carried out for a unit of time at one and the same angular deflection. From what has been discussed so far the categorical conclusion is that the process of generating electrical energy is not unlimited; on the contrary, it is within the framework of exactly determined limits and has its genuine mathematical expression. I must add that however convincing the theoretical portion of this article sounds, the really irrefutable proof of the consistency of the above proposition is the result one gets when making an experiment similar to the one in Fig.8a, which anyone can set up and test. In this test, and to completely convince ourselves in the result, after making the experiment in the manner described above, we can make use of another method, this time changing the conductors’ roles, i. e. the propellant functions will be carried out by the short arm’s big conductor while the generating functions will remain the small conductor’s obligation. Making the experiment in that second way will show us that to sustain the rotation of the small conductor, when we use a given amount of electrical energy from the small conductor to overcome the resistance momentum of the current being fed (as per Lenz’s Rule), we shall have to feed to the big conductor much greater amounts of electrical energy compared to the ones we get, and that would of course be fully meaningless. The practical result yielded by the experiments and expounded by the principal postulates described above and which I hope shall add to scientific knowledge are my chief grounds to categorically state that the clue to solving the energy problem on a global scale has now been found.

**Dzhafer Nuredin Mekhmed**