

Michael Faraday (1791 – 1867) was a master of electricity.  His researches established may important results in electromagnetic theory, including some which are now so taken for granted that Faraday’s name is unfortunately not even thought of in connection with them.


Faraday, though apparently not very sophisticated theoretically, was an amazing experimentalist.  Though I was originally looking for only a single quotation from his articles, I eventually downloaded a half-dozen of his works and I thought I’d discuss their details and their historical import.

We start with what is arguably his most important physical contribution, now known as Faraday’s law.  Faraday’s work opened the door to the discovery of Maxwell’s equations and the identification of light as an electromagnetic wave.  I find it most satisfying to review the experimental work knowing the underlying physical law, so we begin with a qualitative discussion of the “need to know” information concerning electricity, magnetism, and Faraday’s law.

First, we need to say a little bit about electric fields and magnetic fields!  Electric charges are attracted to or repelled from one another, depending upon whether the sign of the charges are of opposite sign or the same sign, respectively.  We can interpret this result as the interaction of one charge with the electric field emanated by the other, which is usually depicted as a ‘flow’ of field emanating from or entering into the charge.  The field flows away from positive charge, and towards negative charge:


An electric charge q which is placed into the electric field will feel a force {\bf F} equal to the product of the electric field (a vector quantity) and the value of the charge itself,

{\bf F} = q {\bf E}.

We won’t go into the specific mathematical form of the electric field.   Suffice to say, a positive charge placed into the field of another positive charge will be pushed away, while a positive charge placed into the field of a negative charge will be attracted.  The study of the forces/fields of unmoving (static) electric charges is known as electrostatics.

Magnetic fields are a little more difficult to explain.  Historically, magnetic forces were considered to be completely different than electric forces, as the only sources of magnetism at first were natural permanent magnets.  This changed in 1820, when Hans Christian Øersted accidentally discovered that an electric current, i.e. moving electric charges, will deflect a magnetic compass needle.  This was the first evidence that electricity and magnetism were actually related to one another.  After hearing of these discoveries, André-Marie Ampère elaborated upon them and formulated the basic principles of magnetostatics: steady (static) electric currents result in magnetic fields which circulate around them:


A long, straight wire carrying current I will have a magnetic field which circulates around its axis, while (more important for our later discussion) a loop of current will have a magnetic field which passes through the middle.  The direction of the field {\bf B} can be determined using the so-called ‘right-hand rule’: if you point the thumb of your right hand in the direction of the current, your fingers curve in the direction that the magnetic field circulates around it.

The force created by a magnetic field is a little more difficult to explain in simple terms; the formula for the force on an electric charge q moving at velocity {\bf v} is given by:


where \times is a vector operation known as the cross product.  For our purposes, it suffices to note that the effect of the cross product is that the magnetic force on a moving charge is perpendicular to both the direction the charge is moving and the direction of the magnetic field.  If the magnetic field is pointing up and a positive charge is moving north, the charge will experience a force to the east (a negative charge will experience a force to the west).

The preceding discussion is essentially the state of understanding of electric and magnetic fields in Faraday’s time: Charges produce electric fields, and charges in electric fields experience electric forces.  Moving charges produce magnetic fields, and moving charges in magnetic fields experience magnetic forces.  Øersted and Ampère’s discoveries had established a link between electricity and magnetism, in that moving electric charges produce magnetic fields.  Faraday solidified the link between the two forces with the  important discovery was that a changing magnetic field produces an electric field!

Without going into too much detail, this phenomenon can be demonstrated as follows: imagine a wire loop attached to an ammeter, a device for measuring electric current.  As we bring a magnet towards the wire loop, we find that a current arises in the loop, but this current appears only while the magnet is moving.  The electric field which creates this current is directly related to the rate of change of the magnetic field flowing through it.  Formally, we may state Faraday’s law as:

The induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.

Current appears only when the number of magnetic field lines (the ‘magnetic flux’) passing through the loop is changing.  This is illustrated below:


A circulating electric field is produced while the magnetic field is growing or shrinking.  It is important to note that the electric field does not depend at all on the overall strength of the magnetic field, or its direction; it only depends on how fast, and in what way, the magnetic field is changing.

It is important to note the direction of the induced electric field.  As we have seen from Ampère’s discovery, a current loop produces a magnetic field.  From the picture above, we can determine that the induced electric field produces a magnetic field which resists the original changing field:


Faraday’s law is the basis for one of the fundamental electrical components, the inductor, which in its simplest form is a helical coil of wire.  When the amount of current running through the wire is changed, this changes the magnetic field running through the center of the helix.  In turn, a counter-current is produced by Faraday’s law which resists the original change:


In essence, an inductor resists changes to the current flowing through it.

Now let us turn to Faraday’s discovery of his eponymous effect, which was reported upon in the Philosophical Transactions of the Royal Society of London, vol. 122 (1832), 125-162.   The entire paper is striking for its clarity and detail, and begins with the reasoning which led his investigations*:


Certain effect of the induction of electrical currents have already been recognised and described: as those of magnetization; Ampere’s experiments of bringing a copper disc near to a flat spiral; his repetition with electromagnets of Arago’s extraordinary experiments, and perhaps a few others.  Still it appeared unlikely that these could be all the effects induction by currents could produce; especially as, upon dispensing with iron, almost the whole of them disappear, whilst yet an infinity of bodies, exhibiting definite phenomena of induction with electricity of tension, still remain to be acted upon by the induction of of electricity in motion.




There’s a lot of information in this introduction, and we will return to some of the details (such as Arago’s magnetic phenomena) later.  Several things are worth pointing out right away.

First, Faraday was motivated to perform his research by the phenomenon of electric induction.  When a positively-charged object is brought close to an electrically neutral object, the positive charges in the neutral object are repelled, and the negative charges attracted.  The details of this process depend on the material, but the net result is that the neutral object has had electrical charges ‘induced’ within it:


Faraday seems to have followed the following reasoning: 1.  Electric charges can induce charge separation in other objects through their electric fields.  2.  Magnetic fields are produced by moving electric charges.  3.  By analogy, might not an electric current therefore induce an electric current in a nearby wire through its magnetic field?  This is a wonderful bit of physical intuition; Faraday clearly saw a strong analogy between the behavior of electricity and magnetism, though the connection turns out to go farther than he initially imagined.

To maximize any possible effect, Faraday wanted to have two very long wires placed very close to one another.  By what seems to be a happy coincidence, Faraday used overlapping helicoids:



A galvanometer is a current measuring device which features a needle deflected by the magnetic field created by the current flowing through the device.  A simplified version of Faraday’s experiment is shown below (neglecting the multiple interconnected helices):


By sending a current through one helix (the black one), Faraday hoped to induce a detectable current through the other (the red one), which he could detect via the galvanometer.  His results were not exactly what he expected, however:



This is the first historical description of Faraday induction!  The use of a helical configuration was convenient, because it maximized the amount of magnetic flux passing through the electrical circuit and hence the amount of current induced.  His initial statements already encapsulate almost every statement of import about Faraday induction.  Induction only occurs when the current is switched on or off (i.e. when the magnetic field produced by that current is changing).  Also, induction goes one way for increasing current, and the opposite way for decreasing current.

Faraday further confirmed the presence of an induced current by replacing the galvanometer with another helix.  If current was flowing through this helix, it would produce a magnetic field, which could in principle magnetize a steel needle placed within.   He found that, if he placed the needle, turned on the system, and removed the needle before turning it off, the needle would be slightly magnetized.  If he instead turned the system on and off before removing the needle, “it exhibited little or no magnetism; the first effect having been nearly neutralized by the second.”  This is also readily understandable: the magnetic fields produced when the system is turned on and off are in opposite directions, and their magnetizing influence will tend to cancel.

Faraday was extremely thorough; the small effect he was observing might still have been due to some quirk of the experimental setup, in particular some sort of discharge related to turning on  the switch.  He therefore produced the effect by a quite different technique, which allowed the current to continually flow:



The system was as shown schematically below:


There are two important observations to take from this new experiment.  First, Faraday induction can be created by moving the inducing wire as well as by changing the current in the inducing wire.  The strength of the magnetic field generated by the inducing wire varies with distance from the wire.  Therefore, by moving the wire towards the ‘induced’ wire, the magnetic field flux at that wire is increased.

Second, Faraday notes that “the induced current was in the contrary direction to the inducing current.”  Though he has not yet formulated it as such, this is the first statement that suggests that the induced current is such that its magnetic field partially cancels any change in the magnetic field around it.

In Faraday’s time, electricity and magnetism were still relatively unexplored topics.  Faraday did not at first rule out that the galvanometer was being affected by means other than electricity, so he attempted to detect the presence of a current by alternative means, initially with little success:

I could obtain no evidence by the tongue, or spark, or by heating fine wire or charcoal, of the electricity passing through the wire under induction; neither could I obtain any chemical effects, though the contacts with metallic and other solutions were made and broken alternately with those of the battery, so that the second effect of induction should not oppose or neutralize the first.

It was clearly a different era of science: most researchers these days would (I hope) hesitate to detect electrical discharges by sticking the wire to their tongue!

This monumental discovery covers only the first six pages of Faraday’s 37 page report!  The next section is just as important as the first, as it explicitly demonstrates the ‘evolution of electricity from magnetism’.  Though it was clear in Faraday’s time that electrical current produced magnetism, it did not necessarily follow that the induction of electrical current already described was an effect arising from magnetism.  Faraday produced another cylinder of helices such as described above, save for the fact that the inner core was constructed of hollow pasteboard, allowing objects to be slid within.  First, Faraday demonstrated that the previously described effects held true for his new cylinder.  Then he introduced a cylinder of soft iron into the middle of the helix.  We let his own words speak for themselves on the next step:

Similar effects were then produced by ordinary magnets: thus the hollow helix just described had all its elementary helices connected with the galvanometer by two copper wires, each five feet in length; the soft iron cylinder was introduced into its axis; a couple of bar magnets, each twenty-four inches long, were arranged with their opposite poles at one end in contact, so as to resemble a horse-shoe magnet, and then contact made between the other poles and the ends of the iron cylinder, so as to convert it for the time into a magnet: by breaking the magnetic contacts, or reversing them, the magnetism of the iron cylinder could be destroyed or reverse at pleasure.


Faraday’s own figure depicting the setup is shown below:


This is a little hard to interpret, so let’s reproduce it with labels:


When the bar magnets are touched to the iron rod, it is magnetized!  This magnetization of the iron is an increase in magnetic flux, which results in a current appearing in the helix which partially counteracts this magnetization.  When the bar magnets are removed, the magnetization was removed, and a current appears in the helix which partially counteracts this demagnetization.

The electrical induction in this case is done completely with magnets and no electrical currents.  However, a ‘circuit’ must still be closed, in this case a magnetic circuit, and it is still possible that something unusual happens on closing the circuit.  To this, Faraday tried the following variation:

But as it might be supposed that in all the preceding experiments of this section it was by some peculiar effect taking place during the formation of the magnet, and not by its mere virtual approximation, that the momentary induced current was excited, the following experiment was mlade. All the similar ends of the compound hollow helix were bound together by copper wire, forming two general terminations, and these were connected with the galvanometer. The soft iron cylinder was removed, and a cylindrical magnet, three quarters of an inch in diameter and eight inches and a half in length, used instead. One end of this magnet was introduced into the axis of the helix, and then, the galvanometer-needle being stationary, the magnet was suddenly thrust in; immediately the needle was deflected in the same direction as if the magnet had been formed by either of the two preceding processes. Being left in, the needle resumed its first position, and then the magnet being withdrawn the needle was deflected in the opposite direction. These effects were not great; but by introducing and withdrawing the magnet, so that the impulse each time should be added to those previously communicated to the needle, the latter could be made to vibrate through an arc of 180° or more.

In other words, a permanent magnet was shoved directly into the center of the helix.  This also is effectively changing the amount of magnetic flux through the system, and resulted in an induced current while the magnet was in motion.

Various larger magnets were employed in place of the pair of bar magnets; it is interesting to note that powerful magnets were presumably hard to come by in that time:


Initially, attempts to demonstrate electrical action other than with the galvanometer were not met with success; however,


This use of frogs and chemicals was not solely for the purpose of ‘doublechecking’ the results.  Researchers had not yet proven conclusively that static electricity, voltaic (chemical) electricity and ‘animal electricity’ were manifestations of the same phenomenon, as they seemed rather different in their details.  Faraday himself would, in a later report, discuss his investigations of their identical origins.

It is worth noting that Faraday’s work was not without some mistakes.  In the third section of his paper, “New electrical state or condition of matter,” he postulates that induction represents a new state of matter:

Whilst the wire is subject to either volta-electric or magneto-electric induction, it appears to be in a peculiar state; for it resists the formation of an electrical current in it, whereas, if in its common condition, such a current would be produced; and when left uninfluenced it has the power of originating a current, a power which the wire does not possess under common circumstances. This electrical condition of matter has not hitherto been recog- nised, but it probably exerts a very important influence in many if not most of the phenomena produced by currents of electricity. For reasons which will immediately appear, I have, after advising with several learned friends, ventured to designate it as the electro-tonic state.

Faraday seems to have initially found the transient nature of the induced current as evidence of some sort of peculiar state of matter, and he spends many pages on it.  However, his publication contains the following footnote at the beginning of the section:

This section having been read at the Royal Society and reported upon, and having also, in consequence of a letter from myself to M. Hachette, been noticed at the French Institute, I feel bound to let it stand as part of the paper; but later investigations of the laws governing these phenomena, induce me to think that the latter can be fully explained without admitting the electro-tonic state. My views on this point will appear in the second series of these researches.

By the time of publication, he had already realized his ‘electro-tonic’ theory was wrong, but since it had been presented at conference, he included the discussion!

The last major portion of the paper concerns the application of Faraday’s discovery of induction to explain an unusual discovery that had previously been made by Arago:


In other words, if one hangs a magnetic needle above a copper disc, and both are unmoving, no force exists between them.  If the plate is rotated, however, the needle tends to get ‘dragged’ along with it; conversely, if the needle is moved, the plate gets dragged along.  Faraday notes,

Upon obtaining electricity from magnets by the means already described, I hoped to make the experiment of M. Arago a new source of electricity; and did not despair, by reference to terrestrial magneto-electric induction, of being able to construct a new electrical machine.

Using the super-powerful permanent magnet of the Royal Society as before, Faraday prepared a copper disc so that its edge would spin between the magnetic poles:


A galvanometer was attached to the disc, and its response studied:


In other words, when the disc is spun, an electrical current flows from the axis of the disc to the rim of the disc!  This again is a current induced by a changing magnetic field:

The experiments described combine to prove that when a piece of metal (and the same may be true of all conducting matter) is passed either before a single pole, or between the opposite poles of a magnet, or near electromagnetic poles, whether ferruginous or not, electrical currents are produced across the metal transverse to the direction of motion; and which therefore, in Arago’s experiments, will approximate towards the direction of radii. If a single wire be moved like the spoke of a wheel near a magnetic pole, a current of electricity is determined through it from one end towards the other. If a wheel be imagined, constructed of a great number of these radii, and this revolved near the pole, in the manner of the copper disc , each radius will have a current produced in it as it passes by the pole. If the radii be supposed to be in contact laterally, a copper disc results, in which the directions of the currents will be generally the same, being modified only by the coaction which can take place between the particles, now that they are in metallic contact.

Basically, a copper disc can be considered a collection of wires, like the spokes of a wheel:


Each wire is passing through a changing magnetic field when it passes the poles of the magnet, and an electric field is therefore induced in the wire!  A quantitative assessment of such problems are now regularly assigned in undergraduate electromagnetism courses.

This paper did not mark the complete body of Faraday’s work on electrical induction.  The experiments are described, and the generality of the effect (its presence in any situation where changing magnetic fields arise) is demonstrated, but the modern formulation of Faraday’s law is not given.  As noted, Faraday was apparently not much of a theorist, though his physical intuition was stunning, as can be seen from the work discussed here.

Before we conclude, we should note a couple of Faraday’s footnotes which fall into the category of “The more things change, the more they stay the same.”  In particular, Faraday has to argue against misrepresentation of his work and argue for the primacy of his work!  In the former case, he notes


Apparently the French scientists attempted to show that Faraday’s work had already been done by Fresnel and Ampere!  Furthermore, Faraday notes at the end of his paper,


Here we see the familiar problem of reporting before publication: Faraday had discussed his experiments before publication, and others had (honestly) reproduced his work.  However, many apparently thought that the later work by Nobili and Antinori was in fact the first!  The history books have managed to get it straight and give Faraday the credit he deserves.

Faraday’s discovery was one of the final breakthroughs that led Maxwell to formulate his famous system of equations, and be led from those equations to the interpretation of light as an electromagnetic wave!  In fact, one can interpret Faraday’s induced currents as the transmission of extremely low frequency electromagnetic waves.  Faraday’s law is also fundamental in the operation of many electrical generators, electric motors, and transformers.

This was a hard paper to discuss, because it is 37 pages and so filled with useful information that almost every page is worth quoting!  Suffice to say that I’ve left out a lot of interesting experimental detail in the interest of sanity: Faraday was a very thorough fellow.

We’ll come back and discuss a number of Faraday’s other discoveries, which range from the practical to fundamental to the visionary!

Update: In a happy coincidence, I only now see that yesterday Jennifer at Cocktail Party Physics wrote a post about Faraday and his work!  Check it out here.


* Note: The original article has numbered paragraphs and numerous references to these paragraph numbers and also to figures.  I have left out these numberings from the original text.


28 Responses to Mr. Faraday’s (most excellent) experimental researches in electricity (1831)

  1. Markk says:

    Cool review! I always felt that Faraday’s experiments as seen by Maxwell really created “modern” physics. We are still using the mathematical formulations today of Maxwell and the idea of field theories. Faraday was the guy that created the clear understandable effects that Maxwell could look at and explain mathematically. If you look at physics like Kelvin, Gibbs, and such after Maxwell it seems like that was the generation that created the tools that still underlie our basic theories today. We look at Newton’s stuff through the lens of field theory today too. Statistical mechanics models from that era are still the basis for our understanding now.

  2. Markk: Thanks for the comment! As I’ll show in a later post, Faraday was one hundred years ahead of his time, at least in one experiment he attempted…

  3. Wow! This is like a free “Giant’s Shoulders” entry!

    • Steven hayes says:

      Needed more information .Thankyou for going to the trouble though its nice to know that Faraday and me share a religion .

  4. erm… I guess all of The Giant’s Shoulders entries have been free…

  5. Babs67 aka the fiancee says:

    PD: Actually, I submitted it to TGS; I just didn’t bother to label it as such, for once…

    And when are YOU going to submit something for TGS?

    *crickets chirping*

  6. stupid freakin’ crickets

  7. this is my question and please reply the answer soon on my given id “why did faraday wind twine in between the turns of copper wire”? and”why did he place calico cloth in between layers?”

  8. carolynberlin says:

    When I was a girl, my father explained electricity to me using an analogy of horses. In my memory of these discussions (which occurred a half century ago), he spoke of Faraday’s horses. Did Faraday ever use such an analogy?

    • I don’t know off the top of my head if Faraday referred to horses, though he may have in his popular lectures. I’ll take a look through those lectures that I have and see if there’s anything mentioned!

  9. prasanna says:

    why did faraday wind twine and calico paper in his experiment’ am not satisfied with above ans.

    • I’m not sure what else to say about it — in Faraday’s time, there was no such thing as insulated wires like we can purchase in the stores today. He would have been working with bare metal wires, and touching these bare wires together would result in a short-circuit and wreck the whole experiment. Faraday separated the wires with non-conducting twine at a given radial distance, and used paper to separate multiple layers of solenoids; he was therefore able to pack many layers of wire together without having individual wires touching.

  10. Pingback: A Michael Faraday Christmas: “Forces of Matter”! | Skulls in the Stars | The Chemistry Matter Site

  11. glenmartin says:

    In your explanation of the cross product you got something backwards: “If the magnetic field is pointing up and a positive charge is moving north, the charge will experience a force to the west (a negative charge will experience a force to the east).”

    Following the right-hand rule, with fingers straight point your hand in the direction of the velocity vector (north), then curl the fingers toward the direction of the B vector (up), the thumb then points in the direction of the resulting force (east).

  12. Jacob B. says:

    This is a great article on Faraday’s work, and thank you for including the figures (which seem to be missing from Project Gutenberg’s edition of the Experimental Researches). But I think that Faraday deserves more credit as a theorist than he is given in most places, including this article, and it does him an injustice to keep labelling him a poor theorist. He may not have explored physical laws mathematically, as we are now used to it being done, but he was also not merely an experimentalist, in the sense that he did not simply perform and report on experimental results. Theory and math are not inseperable, and although math is an extremely powerful tool for exploring theory, it is not the only one.

    As is evident from reading his Experimental Researches and, Faraday was certainly crafting a theory of electromagnetism clearly in his mind, and this is how his experiments were guided so insightfully. It’s true that in some cases he made intuitive leaps which led him to perform some of his more revolutionary experiments, like suspecting that magnetism should induce currents the way static fields induce charge, or later when he discovers the “Faraday Effect” of magnetic fields affecting the polarization of light in glass just on the suspicion that magnetism ought to affect light somehow. That definitely shows an experimental approach of hazarding a guess and then testing carefully to see how it works out. But his theoretical mind shows through in his analysis, and in the success of his experiments. What comes across is that he was a talented theorist whose ability to defend and communicate his ideas was severely hobbled by a lack of familiarity with math.

    One example would be his rejection of the aether. Here is an excerpt from one of his letters:


    This is a relatively modern view of electromagnetic waves. Credit is given to Maxwell for showing mathematically that the fields satisfy the wave equation and can propagate this way, and for showing that it matches the speed of light, but Faraday could already tell by thinking about field lines that light could be propagate as a disturbance in the electromagnetic field. This was grounded in the theoretical understanding that he had developed of field lines connecting charges; he didn’t perform an experiment to show that it worked this way. As well, he reasons that light propagates as a transverse wave, whereas an elastic aether (as was the hypothesis) could not propagate only transverse waves alone. Again this is a theoretical perspective, but non-mathematical and so it doesn’t seem to have been highly valued.

    Often Faraday tended to think of nature very differently than most of his contemporaries, and a result of that was the amount of caution and care that he puts into his experiments, and his tendency to interprets his experimental results with so much reluctance and skepticism. The theory stayed in his mind most of the time, and guided him in his experiments, and he only reported the theory when he had amassed enough evidence to defend his views.

    L. Pearce Williams, in his biography of Faraday, writes of Faraday and Sir Humphry Davy:

    “In both men’s papers, the reader was informed, almost casually, of the theoretical framework within which new results were being reported. Only rarely, however, was this framework insisted upon. The result has been that Davy and Faraday are characterized in the history of science as empiricists without any general theoretical foundation of any importance. This, it will be shown, is both false and misleading.”

    I would say that Faraday used experiments as a substitute for math in making a case for his theories. But that does not make him a poor theorist. Theory was still his path to discovery, and experiment was just the paving stones he used.

  13. thanks and heartiest congrats for all who took lots of pains in compilig all these and make it available to readers like me. Please keep it up ;
    thanks once again.
    one small suggestion/observation..Faradays`s efforts lead to introfduction of ELECTRICAL TRANSFORMERS., which are most essential in Electrical Power Transmission, Distribution and Utilisation.Without Transformers, man would have been far far behind where he is standing today.
    Hats of to MICHAEL FARADAY !!

  14. Joseph says:

    Thank you for this extensive post on Michael Faraday, I am currently answering some questions in relation to the principles and applications of electromagnetic induction. You have saved me a considerable length of time.

  15. Pingback: Shocking: Michael Faraday does biology! (1839) | Skulls in the Stars

  16. Gary Boothe says:

    I read somewhere that after one of Faraday’s lectures demonstrating electricity he was approached by the mayor of London who said, “A very interesting demonstration of electricity, Mr. Faraday, but what good is it?” Is this true?

  17. collins odhiambo says:

    thanks for giving as more details of Mr Faraday,but,did he left his grandchildren who is a scientist?

  18. Where did you buy your Faraday disk?

    If an iron sphere spins as it “falls” due to gravity, through earth’s magnetic field, would it pick-up an electromagnetic charge?

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  20. Pranav says:

    Thank you for helping me in my project

  21. Mr. Martin WØAUU for 60 years says:

    Faraday’s law of induced voltage in a coil says EMF = T turns in the coil times F for the strength of the magnet times f little f for the FREQUENCY of change from north pole to south pole times 2, my question is, what happens IF we use ALL THE SAME POLE ? Then f the frequency is Ø and Ø times any number is still Ø, BUT we know that can not be right because if you pass all the same pole magnet past a coil, each time a magnet passes it WILL make voltage in that coil

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