A RE-LOOK INTO FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION BASED ON ELECTRON THEORY

EDITOR: B. SOMANATHAN NAIR

ABSTRACT: Michael Faraday enunciated the law of electromagnetic induction in 1831. This law states that whenever a conductor cuts a magnetic field, an electromotive force (EMF) is induced in it. This law has been accepted by the scientific world as such without any modification for nearly two centuries now. In this paper, we investigate the completeness of the statement of Faraday’s law and suggest some modifications in its statement so that it explains the action of what is known as (electro) magnetic induction. 

1.    INTRODUCTION

Faraday’s law of electromagnetic induction (or simply, magnetic induction¹) states that whenever a conductor cuts a magnetic field, an electromotive force (EMF) is induced in it. Everybody in the scientific world has accepted this law as such without any question being asked about its completeness. There is no doubt about the truthfulness and validity of this law. However, a couple of questions arise in this case which nobody has raised or answered so far:

      1. What is electromagnetic induction?

      2. What is the speed with which induction takes place in a conductor?

In this paper, we attempt to give answers to these important basic questions and suggest some more aspects that may be included in the Faraday’s law.

2. EXPERIMENTAL DEMONSTRATION OF THE PROCESS KNOWN AS ELECTROMAGNETIC INDUCTION

      Consider an experiment in which an ac voltage (or, EMF) is applied across the terminals of a straight metallic (say, copper) conductor AB as shown in Fig. 1. A straight-wire conductor is used here for the simplification of explanation.

    During positive half-cycles (PHCs) of the input voltage, when the top terminal A of the conductor is positive with respect to its bottom terminal B, free electrons in the conductor move upwards from B to A, which results in a primary electron current I_1e flowing from B to A. This is illustrated in Fig. 1 by the green-colored dotted-line block arrow shown as superimposed over conductor AB. In Fig. 1, we have also shown the conventional primary current I_1p corresponding to I_1e, indicated by the orange-colored block arrow. It must be remembered that the direction of electron current (due to the flow of negative charges) and that of the conventional current (due to the flow of positive charges) corresponding to this electron current are mutually opposite to each other. This is the reason why the green-colored and orange-colored block arrows are shown in opposite directions.

      Now, since electrons are also tiny magnets (their natural dual property), as they move upwards, the magnetic field associated with them (indicated by the blue-colored dotted-line circular arrows) will also move upwards. It may be noted that this magnetic field is oriented in a direction perpendicular to that of the electron flow, as illustrated in Fig. 1. It may also be noted that since the applied ac voltage is sinusoidal, the resultant primary current and the generated primary magnetic field are sinusoidal with their respective frequencies the same as that of the input voltage. This means that, if the input voltage is of 50 Hz, then the generated alternating current and ac magnetic field are also of 50 Hz.

     Let us now assume that a second copper conductor CD (with terminals C and D being connected through a suitable load resistance R_L) be placed inside the same magnetic field, as shown in Fig. 1. It can be easily observed that in this case, the magnetic field produced by the electron current flow I_1e in the primary conductor AB in turn interacts with the free electrons in the secondary conductor CD and deflects them so that they move in a downward direction through it (i.e., CD). This reversal of current flow is quite natural because it is the upward motion of electrons in AB that produced the magnetic field; this field in turn produces the motion of electrons in CD. Since this is a reverse process of the first action, naturally the direction of the current flow in CD must be opposite to that in AB. The reversed secondary electron current I_2e and the conventional current (I_2p) corresponding to it are indicated in Fig. 1 using the cyan-coloured and the blue-coloured block arrows, respectively. It may further be noted that both I_2e and I_2p possess the same frequency as that of I_1e.

It can also be seen that the generated primary magnetic field is an alternating quantity, it spreads around the primary conductor with the same frequency as that of the primary current and at a velocity equal to that of the light. In this connection, we remember that the magnetic force generated by a magnet can be felt at places far away from its original location (natural property of a magnet); the more powerful the magnet, the more the distance at which its effect is felt. Also, if this magnetic field is alternating with a frequency of f Hz, then its effect will be felt at a distance of 3×10⁸ meters at the same frequency of f Hz after 1 second. This means that current is generated (or, induced) in the secondary coil with a frequency of f Hz and at a speed equal to that of the light. It may further be noted that it is the magnetic field (in the form of waves) that is spreading through space; there is no electric-field component attached to this. Actually, electric part of these magnetic waves occurs only when they are intercepted (or cut) by a conductor and then they induce a current in it. Thus the term electromagnetic wave is a misnomer. It must be actually redesignated as magnetic wave and not as electromagnetic wave.¹

From the discussions given above, we observe that when a conductor is placed inside a varying magnetic field, a varying current of the same frequency is produced in it due to the deflection of free electrons in it by that magnetic field. This clearly suggests that it is an alternating current, and not an EMF, that is generated in a conductor when it is placed in an alternating magnetic field. The EMF mentioned in the Faraday’s law can be seen to be the potential drop that is produced in the conductor due to this current flow. However, due to long-term usage, the term magnetic induction can be used to indicate the generation of an electromotive force (voltage) also.

Figure 2 shows the situation during negative half-cycles (NHCs) of the applied ac voltage. During the negative half-cycles, terminal B becomes positive with respect to terminal A and hence electrons in the conductor move downwards reversing the direction of current I_1e through AB. In this condition, we notice that the associated magnetic field has also reversed. This in turn results in an upward motion of electrons through conductor CD. Thus we find that current I_2e also gets reversed in this case, as shown in Fig. 2. 

          

3.    STATE OF AFFAIRS WHEN THE SECONDARY IS OPEN

In Section 2, we had assumed that the secondary is shorted through a load resistance. A pertinent question arises here: What will happen if the secondary terminals are kept open? In fact, original Faraday’s law states that a voltage is induced in the secondary when a magnetic field is cut by that conductor. This statement suggests that the secondary is open.

According to Section 2, to have a current flowing through it, the secondary must form a closed path; then only electrons in that coil can move to produce the current. However, how can a current flow through a conductor if it is open?

  The problem given above can be solved by considering the fact that there always exists a very low-value parasitic capacitance with air as dielectric across the terminals of a conductor carrying currents of opposite polarity (a basic property of a capacitance). Based on this property, we find that there always exists a parasitic capacitance C_P across secondary terminals C and D as shown in Fig. 3. It can be easily seen that it is this capacitance C_P that completes the required secondary path through which the secondary current is flowing. This current in turn develops a voltage drop across CD, which forms the open-circuit secondary voltage (as per Faraday’s law).

A similar action as given above takes place during the negative half-cycles. The only difference is that, as illustrated earlier, the directions of currents reverse in this case from those shown in Fig. 3. However, no figure is given for this case, since it is similar to Fig. 2, with R_L replaced with C_P.

It is found that C_P will be usually in the range of a few picofarads so that the secondary current will be usually very small (maybe on the order of a few picoamperes). The following calculations will prove this fact.

Let the secondary voltage be equal to 10 volts and let C_P be equal to 10 pF. Then, for a 50-Hz ac, the capacitive reactance X_CP = 1/2πfC = 318.3×10⁶ ohms. The secondary current, therefore, will be 10/318.3×10⁶ = 31 nanoamperes (approximately). This current is usually considered as negligible. However, it may be noted that if the input frequency is raised to 1 GHz, the secondary current will be about 0.6 ampere, which is a large value compared to 31 nA.

4.    SUGGESTED NEW ADDITIONS TO BE INCORPORATED INTO THE EXPLANATION OF ORIGINAL FARADAY’S LAW

      We now suggest that the following points may be incorporated into the explanation of original Faraday’s law so that it may become more clarified.

      Whenever a conductor cuts a magnetic field, free electrons in it get deflected by the field producing a current flow through it. This current will be a transient direct-current spike if the magnetic field is a DC field; it will be an alternating current if the field is an ac magnetic field and continuous if the field is continuous. This current completes its path through the parasitic capacitance existing across the terminals of the conductor and develops a potential (or EMF) across its terminals. 

      As an alternative to the above, we may state: An ac current flowing through a conductor produces an ac magnetic field which spreads in the space surrounding it with a velocity equal to that of the light and deflects the free electrons in another conductor placed inside the same magnetic field; this produces an ac motion of the electrons resulting in an ac current being driven through it in a direction opposite to that in the first conductor; this ac current in turn produces an ac voltage drop across the terminals of the second conductor, which becomes the induced EMF in it.

The statements given above can be elaborated into the following actions, which may be used in explaining the Faraday’s law.

1. A DC magnetic field will produce a dc current spike or transient in conductor that cuts it.

2.  If the magnetic field is alternating and continuous, the generated current will also be alternating and continuous.

3.  In both the cases mentioned above, the current will flow through a path completed by the parasitic capacitance existing across the terminals of the conductor; producing a voltage drop (or EMF) in it.

4. Alternatively, if the magnetic field is generated by applying an ac voltage across a conductor (called the primary conductor), then free electrons in it gets deflected by the generated field producing an alternating motion of the electrons. This produces an ac current that flows through the primary conductor.

5. Since electrons are also tiny magnets (dual property), when they move through a conductor, they produce a moving ac magnetic field surrounding it in a direction perpendicular to the axis of the conductor.

6. The generated ac magnetic field spreads through the space surrounding the primary conductor with a velocity equal to that of the light.

7. Since this magnetic field is alternating in nature, it will interact with the electrons in a second conductor (called the secondary conductor) placed inside the same field and deflect them magnetically.

8. The deflection of electrons in the secondary conductor in turn produces an alternating current in it, when the secondary is closed through a connected load.

9. The direction of this secondary current can be seen to be opposite to that of the primary current. This is because the spreading magnetic field is produced by the primary current; this magnetic field in turn produces the secondary current. Since these two actions are mutually opposite to each other, direction of the current flow in the secondary has to be (and will be) naturally opposite to that of the current flow in the primary.

10. If the secondary is open (instead of a closed one, as proposed in the original Faraday’s law), then the secondary can be assumed to form a closed path through the invisible parasitic air capacitance of very low value that will always exist across the open-circuited secondary terminals. The secondary ac current (of very low value) will then flow through this completed path and produce a voltage drop across the secondary terminals, which will then act as the open-circuit secondary voltage (since the parasitic capacitance is invisible).

11. From the above arguments, it is also clear that current will be generated in all the conductors placed inside the same magnetic field.

12. In actual practice, straight conductors are replaced with multi-turn coils.

5.    SUMMARY

Through this article, we have introduced a few links that we feel are missing in the original Faraday’s law. In particular, we have:

1.  Given some more explanation required to define the process known as electromagnetic induction.

2.   Specified the speed with which induction takes place in a second conductor.

3. Explained on how the direction of the induced secondary current gets reversed with respect to the direction of its generating current.

4.   Given an explanation on how magnetic induction produces a voltage across an open-circuited secondary.

5.   Mentioned the fact that current gets induced in all the conductors placed inside the same primary magnetic field.

6.    ACKNOWLEDGEMENTS

It is specially mentioned here with thanks that the figures shown in this article are drawn using the DRAWING TOOLS available in the Microsoft word software. It may be noted that these tools are extremely useful to prepare drawings in two and three dimensions. In all our articles, we shall be using these tools. We acknowledge our gratitude to the Microsoft Corporation for creating this excellent software package.

7. REFERENCE

1. B. Somanathan Nair, P. S. Chandramohan Nair, S. R. Deepa, N. Anand: "Some New Perceptions on the Magnetic Field and the Radiating Properties of Antennae", IEEE International Workshop on Optical Networking Technologies and Data Security (ONTDS), 2014.