electromagnetic waves experiment

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Heinrich Hertz and the Successful Transmission of Electromagnetic Waves

Heinrich Hertz (1857 – 1894)

On November 13 , 1886 , German physicist Heinrich Hertz succeeded to transmit electromagnetic waves from a sender to a receiver in Karlsruhe .  Hertz conclusively proved the existence of the electromagnetic waves theorized by James Clerk Maxwell’s electromagnetic theory of light.[4] The unit of frequency – cycle per second – was named the “ hertz ” in his honor.

“The rigour of science requires that we distinguish well the undraped figure of Nature itself from the gay-coloured vesture with which we clothe her at our pleasure.” — Heinrich Hertz, as quoted by Ludwig Boltzmann in a letter to Nature (28 February 1895)

Family Background and Education

Heinrich Rudolf Hertz came from a distinguished Hanseatic family. His father Gustav Ferdinand Hertz (original name David Gustav Hertz, 1827-1914) came from a Jewish family, but converted to Christianity. He had a doctorate in law, was a judge since 1877 and from 1887 to 1904 senator and president of the Hamburg administration of justice. The mother Anna Elisabeth née Pfefferkorn was the daughter of a garrison doctor. Hertz graduated from high school at the Johanneum in Hamburg and then prepared himself for engineering studies in a design office in Frankfurt am Main. He broke off his studies in Dresden after the first semester because he was only enthusiastic about the mathematics lectures there. After one year of military service, he began to study mathematics and physics at the Technical University of Munich.

In 1878 he moved to the Friedrich-Wilhelms-Universität in Berlin. He received his doctorate at the age of 23 with a thesis on the rotation of metal spheres in a magnetic field and remained with Hermann von Helmholtz in Berlin for two years as a research and lecture assistant.[5] In 1883 Hertz became a private lecturer in theoretical physics at the Christian-Albrechts-Universität zu Kiel. From 1885 to 1889 he taught as a professor of physics at the Technical University of Karlsruhe.

The Transmission of Radio Waves

In Karlsruhe, Hertz experimented with Riess spirals and he noticed that discharging a Leyden jar  [6] into one of these coils would produce a spark in the other coil. The scientist came up with an idea to build an apparatus and intended to prove Maxwell’s theory. Hertz used a Ruhmkorff coil -driven spark gap and one-meter wire pair as a radiator. Capacity spheres were present at the ends for circuit resonance adjustments. His receiver was a simple half-wave dipole antenna with a micrometer spark gap between the elements. This experiment produced and received what are now called radio waves in the very high frequency range.

The first spark gap oscillator built by Heinrich Hertz around 1886

The scientist proceeded to conduct a series of experiments between 1886 and 1889, which would prove the effects he was observing were results of Maxwell’s predicted electromagnetic waves. He further discussed his results in his paper On Electromagnetic Effects Produced by Electrical Disturbances in Insulators . Heinrich Hertz sent a series of papers to Helmholtz at the Berlin Academy, including papers in 1888 that showed transverse free space electromagnetic waves traveling at a finite speed over a distance. In his device, the electric and magnetic fields would radiate away from the wires as transverse waves. Hertz had positioned the oscillator about 12 meters from a zinc reflecting plate to produce standing waves. Each wave was about 4 meters long. Using the ring detector, he recorded how the wave’s magnitude and component direction varied. Hertz measured Maxwell’s waves and demonstrated that the velocity of these waves was equal to the velocity of light. He further measured the the electric field intensity, polarity and reflection of the waves. These experiments established that light and these waves were both a form of electromagnetic radiation obeying the Maxwell equations.

Further Research

The external photoelectric effect discovered by Alexandre Edmond Becquerel in 1839 was also studied by Hertz in 1886. One year later, this investigation was continued by his assistant Wilhelm Hallwachs (Hallwachs effect). The effect played a special role in Albert Einstein ‘s formulation of the light quantum hypothesis in 1905.

Heinrich Hertz’s proof of the existence of airborne electromagnetic waves led to an explosion of experimentation with this new form of electromagnetic radiation, which was called “Hertzian waves” until around 1910 when the term “radio waves” became current.  Researchers like Oliver Lodge , Ferdinand Braun , and Guglielmo Marconi employed radio waves in the first wireless telegraphy radio communication systems, leading to radio broadcasting, and later television.

From 1889 he was professor of physics at the Rheinische Friedrich-Wilhelms-Universität Bonn, after rejecting appointments to Berlin, Giessen and America. In 1892 Hertz was diagnosed with Wegener’s granulomatosis after a severe migraine attack, in 1894 he died of it in Bonn.

References and Further Reading:

• [1]  Robertson, O’Connor.  “Heinrich Rudolf Hertz” .  MacTutor . University of Saint Andrews, Scotland .
• [2]  Heinrich Hertz at Famous Scientists
• [3]  Heinrich Hertz at Britannica Online
• [4]  James Clerk Maxwell and the Electromagnetic Fields , SciHi Blog
• [5]  Hermann von Helmholtz and his Theory of Vision , SciHi Blog
• [6]  The Leyden Jar Introducing the Age of Electricity , SciHi Blog
• [7] Heinrich Hertz at Wikidata
• [8]  How Heinrich Hertz Discovered Radio to Validate Maxwell’s Equations ,  Kathy Loves Physics & History  @ youtube
• [9]  Susskind, Charles. (1995).  Heinrich Hertz: A Short Life.  San Francisco: San Francisco Press.
• [10]  Hertz, H. (1882).  “Ueber die Verdunstung der Flüssigkeiten, insbesondere des Quecksilbers, im luftleeren Raume” .  Annalen der Physik .  253  (10): 177–193.
• [11]  “Hertz, Heinrich Rudolf”  .   Encyclopædia Britannica . Vol. 13 (11th ed.). 1911. pp. 400–401.
• [12] Armin Hermann :  Hertz, Heinrich Rudolf.  In:  Neue Deutsche Biographie  (NDB). Band 8, Duncker & Humblot, Berlin 1969,  ISBN 3-428-00189-3 , S. 713 f.
• [13] Robert Knott:  Hertz, Heinrich .   In:   Allgemeine Deutsche Biographie   (ADB). Band 50, Duncker & Humblot, Leipzig 1905, S. 256–259.
• [14] Timeline for Heinrich Hertz, via Wikidata

Tabea Tietz

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Famous Scientists

How Heinrich Hertz Discovered Radio Waves

In November 1886 Heinrich Hertz became the first person to transmit and receive controlled radio waves.

Considering how indispensable his wireless transmissions quickly became, it seems a little odd looking back that he had no practical purpose in mind for the radio or Hertzian waves he discovered.

His research was focused solely on discovering if James Clerk Maxwell’s 1864 theory of electromagnetism was correct.

A Young Man in a Hurry

The first time Hertz thought seriously about proving Maxwell’s theory was in 1879, when he was a 22 year-old student in Berlin. He decided against it. It seemed too hard, and anyway he wanted to concentrate on completing his doctorate.

In 1883, after getting his first lecturing job, he revisited Maxwell’s theory. He wrote an impressive paper, reworking the theory mathematically.

In 1885 he moved to the University of Karlsruhe as a full professor of experimental physics. Now he decided the time was ripe to look for a way to prove Maxwell’s theory.

(We have more details of Hertz’s life here .)

A Spark of Genius

In October 1886 Hertz saw an electrical spark, starting a train of thought that would end up transforming the world.

Riess Spirals. Hertz saw sparks fly between the small metals balls.

Hertz became fascinated by sparks.

He started generating them using a piece of electrical equipment called an induction coil. (A car’s spark plugs are powered by an induction coil. The induction coil transforms low voltage dc electricity coming from a car’s battery into high voltage ac electricity. This electricity crosses a small air gap at regular intervals as a spark – i.e. you have a spark plug.)

You can see a diagram of an induction coil connected to a spark-gap below.

Hertz spark testing circuit.

He used the induction coil to generate high voltage ac electricity, producing a series of sparks at regular intervals at the main spark-gap.

Hertz found that when sparks flew across the main gap, sparks also usually flew across the secondary gap – that is between points A and B in the image; Hertz called these side-sparks .

He found the behavior of the side-sparks highly thought-provoking.

He varied the position of connection point C on the side-circuit. The only way he could stop side-sparks being produced was to arrange the apparatus so the length of wire CA was the same as CB.

Given that the electricity was ac, this suggested to Hertz that voltage waves were separately racing through the wire along paths CA and CB.

If the distances CA and CB were the same, then the same voltage must reach points A and B at the same time. The electrical waves in CA and CB were said to be in phase with one another, so sparks could not be generated. Sparks could only be generated if there was a large voltage difference between points A and B.

Distances CA and CB are equal. Voltage waves reach the spark-gap in phase with one-another. There is no voltage difference between A and B, so no sparks jump over the gap.

Distances CA and CB are not equal. Voltage waves reach the spark-gap out of phase with one-another. There is a voltage difference between A and B, so sparks jump over the gap.

Perfectly Behaved Electric Waves

He pictured waves of electric charge moving back and forth, creating a standing wave within the wire.

In other words, he believed the circuit was vibrating like a tuning fork at its natural, resonant frequency. He thought he now had a circuit in resonance.

Of course, in Hertz’s circuit the vibrations were not of sound, they were vibrations of electric charge.

It’s worth bearing in mind that resonance is not actually needed for electromagnetic waves to be produced – they’re produced whenever electric charges are accelerated.

The importance of resonance is that if a receiver has the same resonant frequency as a transmitter, the incoming electromagnetic waves have a much stronger effect on it. This is similar to the situation in which an opera singer shatters a champagne glass because its resonant frequency is the same as the note she sings.

Aware that the frequency of electrical vibrations and hence resonance is determined by electrical properties called inductance and capacitance, Hertz looked more closely at these factors in the circuit.

Breaking Away

Hertz decided to break the hard-wired connection between the main spark circuit and the side-spark circuit, as shown in the image.

He also arranged the capacitance and inductance of the main circuit so its resonant frequency was 100 million times a second. Today we would write this vibration frequency as 100 MHz. (The unit of frequency is, of course, the hertz (Hz), named in Heinrich Hertz’s honor.)

According to Maxwell’s theory, the main circuit would then radiate electromagnetic waves with a wavelength of about a meter.

The actual apparatus is shown below.

Producing and Detecting Radio Waves

In November 1886 Hertz put together his spark-gap transmitter, which he hoped would transmit electromagnetic waves.

Hertz’s spark-gap transmitter. At the ends are two hollow zinc spheres of diameter 30 cm which are 3 m apart. These act as capacitors. 2 mm thick copper wire is run from the spheres into the middle, where there is a spark-gap. Today we would describe this oscillator as a half-wave dipole antenna.

For his receiver he used a length of copper wire in the shape of a rectangle whose dimensions were 120 cm by 80 cm. The wire had its own spark-gap.

Hertz applied high voltage a.c. electricity across the central spark-gap of the transmitter, creating sparks.

The sparks caused violent pulses of electric current within the copper wires leading out to the zinc spheres.

As Maxwell had predicted, the oscillating electric charges produced electromagnetic waves – radio waves – which spread out at the speed of light through the air around the wire.

Hertz detected the waves with his copper wire receiver – sparks jumped across its spark gap, even though it was as far as 1.5 meters away from the transmitter. These sparks were caused by the arrival of electromagnetic waves from the transmitter generating violent electrical vibrations in the receiver.

This was an experimental triumph. Hertz had produced and detected radio waves.

Strangely, though, he did not appreciate the monumental practical importance of his discovery.

In fact Hertz’s waves would soon change the world. By 1896 Guglielmo Marconi had been granted a patent for wireless communications. By 1901 he had made a wireless transmission across the Atlantic Ocean from Britain to Canada.

By the early 1900s technically minded people were building their own spark transmitters at home. Even children got in on the act, with instructions to build a transmitter appearing in a craft book for boys in 1917.

Goodbye to Sparks By the late 1920s most radio transmitters were using vacuum tubes rather than sparks to generate radio waves. And then the vacuum tubes were abandoned in favor of transistors.

Scientists and engineers have continued to innovate quickly in the field of radio technology. Radio, television, satellite communications, mobile phones, radar, and many other inventions and gadgets have made Hertz’s discovery an indispensable part of modern life.

Author of this page: The Doc Images digitally enhanced and colorized by this website. © All rights reserved.

Further Reading Heinrich Hertz Electric Waves Macmillan and Co., 1893

More from FamousScientists.org:

November 17, 2016 at 12:30 am

Its good to read history of humankind. It makes me realize there is no limit to what we are to discover.Lots of love for this site creators

June 8, 2016 at 3:03 pm

Great people, great world. Scientists are immortalised through history and their inventions. Great work!

May 11, 2016 at 9:20 pm

Thank you! I had wondered how something so invisible had been discovered. Not only do you it explain it well, but I see how a love and understanding of music ( tuning fork), and the ability to “play” contributed to this discovery.

April 16, 2016 at 11:12 pm

I have recently come across this website and found it very much useful and inspiring. WhenevernI get some free time out of my work, I start reading the stuff. Thank you for putting a history of the modern scientists together in one place.

Regards Samiran

March 13, 2016 at 7:29 am

I find this site very useful, thanks a lot. A must see website for science s fan.

December 1, 2015 at 4:28 pm

Thank you so much for all these biographies in one place.You save me a great amount of time reviewing all Electromagnetic contributors.

December 2, 2015 at 1:17 pm

Hey, I’m glad you found them helpful, and thanks for leaving the kind words 🙂

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Milestones : First Generation and Experimental Proof of Electromagnetic Waves, 1886-1888

• 3 Street address(es) and GPS coordinates of the Milestone Plaque Sites
• 4 Details of the physical location of the plaque
• 5 How the plaque site is protected/secured
• 6 Historical significance of the work
• 7 Features that set this work apart from similar achievements
• 8 Significant references
• 9 Supporting materials

First Generation and Experimental Proof of Electromagnetic Waves, 1886-1888

In this building, Heinrich Hertz first verified Maxwell's equations and prediction of electromagnetic waves in 1886-1888. He observed the reflection, refraction and polarization of the waves and, moreover, the equality of their velocity of propagation with the velocity of light. His 450 MHz transmitter and receiver demonstrated the fundamentals of high-frequency technology.

Street address(es) and GPS coordinates of the Milestone Plaque Sites

, Kaiserstrasse 12, 76131 Karlsruhe, Germany 49.009515, 8.41233 (Heinrich-Hertz-Auditorium)

Details of the physical location of the plaque

The plaque is mounted outside the Heinrich–Hertz-Auditorium next to the sculpture of Heinrich Hertz.

How the plaque site is protected/secured

The plaque site on KIT campus is open to the public.

Historical significance of the work

The generation of electromagnetic waves is one link in a chain of historic milestones connected with the names of Michael Faraday, James Clerk Maxwell, Heinrich Hertz and Guglielmo Marconi. Hence, its historic significance is two-sided. Hertz verified Maxwell´s theory against the then prevailing views of electromagnetic phenomena and at the same time he opened for Marconi the gateway to the new world of radio and wireless services. Based on the work of Jean-Baptiste Biot, Félix Savart and others the prevailing theory – especially on the European continent – interpreted the electromagnetic phenomena as long-range effects passing instantaneously over the space between charges, currents and magnets. This was supported by the fact that Biot-Savart´s force law showed the same spatial structure as Newton´s law. In opposition to this Faraday postulated his conception of short-range effects in electric and magnetic fields, which propagate with a finite velocity through the space. Maxwell presented Faraday´s conception in mathematical form. As a solution of his field equations he obtained electromagnetic waves propagating with the velocity of light. Hence, Maxwell´s theory asserted the existence of electromagnetic waves and the identity of light with them. However, the question whether this forecast is true or false remained unanswered for two decades. In 1879, initiated by Hermann von Helmholtz, the Academy of Sciences in Berlin, Germany opened a competition for an experimental decision between the two contrary theories of electrodynamics. But only six years later when Hertz left the University of Kiel and became Professor of Physics at the Technische Hochschule Karlsruhe the solution of this problem seemed feasible to him. Here the laboratory facilities including a pair of so-called Ries’s coils were much superior to those at Kiel and he started his experiments. The main problem was how to obtain reactions with very high frequency. He constructed a resonant circuit with both, very small capacitance and inductance by a dipole loaded with two 30 cm diameter spheres made of zinc sheet. The excitation was realized by a spark discharge in the center of the dipole. This arrangement radiated the electromagnetic waves quite well. With a circular wire, a loop antenna, likewise interrupted by a small gap, electromagnetic waves were received and caused a spark discharge. With this configuration Heinrich Hertz was able to detect electromagnetic waves up to a distance of 18 meters. Hertz finally achieved stationary waves with frequencies of 450 MHz by interference of incident and reflected waves. This made it possible to measure the wave length and therewith the velocity of wave propagation. Moreover he could distinguish electric and magnetic fields and their directions, which was the basis for later radio direction finding. (The original apparatus built by Heinrich Hertz is in the Deutsches Museum, Munich in the permanent physics exhibition.) Although Heinrich Hertz did not foresee the consequences of his experimental results with electromagnetic waves, with his experiments and his invention of radio frequency transmitters and receivers he accomplished the fundamentals of high-frequency technology. His experiments, including the invented equipment, were the basis for RF application for communication and Radar. Guglielmo Marconi, Ferdinand Braun, Christian Hülsmeyer and many others based their technologies and inventions on Heinrich Hertz’s results. And his name was in 1960 adopted for worldwide use as the SI unit name for frequency: Hz.

Features that set this work apart from similar achievements

After the competition for an experimental decision between the opposing theories of electrodynamics had been opened in 1879 by the Academy of Sciences in Berlin, very probably there must have been great interest and diverse attempts to participate in this. Heinrich Hertz himself instantly seized this task. He calculated the necessary prerequisites for successful experiments but at that time he came to a negative result. Besides this there had been a number of earlier experiments drawing sparks from conductors in the vicinity of electric discharges (see Charles Susskind, Heinrich Hertz: A Short Life), the earliest already prior to the publication of Maxwell´s Treatise in 1873. In 1842 Joseph Henry already noted the oscillatory nature of spark discharge and presumed that light is an electromagnetic phenomenon. In 1870 Wilhelm von Bezold discovered in his experiments on electric discharge that electricity is transmitted along a wire with a finite velocity. In 1875 Thomas Alva Edison refused the electrical nature of the spark phenomenon and supposed a new force behind it. But this hypothesis was in 1876 experimentally disproved by Eli Thompson. In 1879 David Edward Hughes discovered that sparks would generate a radio signal, but did not report this until later. Moreover, Hughes apparently did not properly understand the operation of the transmissions, which he observed. However, all these experiments could not succeed in the generation and detection of free electromagnetic waves. In his speech in commemoration of Herrmann von Helmholtz on December 14, 1894 Wilhelm von Bezold stated that this was “kept in reserve to Hermann von Helmholtz´s greatest and most ingenious scholar Heinrich Hertz”.

Significant references

[1] Heinrich Hertz, “Gesammelte Werke“, J. A. Barth, Leipzig 1894/95. [2] Heinrich Hertz, “Electric Waves: Researches on the Propagation of Electric Action with Finite Velocity through Space”, authorized English translation by D. E. Jones. New York, Dover, 1962,-XV. (Dover books on history of science and classics of science). [3] Heinrich Hertz, “Erinnerungen, Briefe, Tagebücher“, edited by Johanna Hertz. Akademische Verlagsgesellschaft Leipzig, 1927. The English translation is: Heinrich Hertz,

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Discovering the Electromagnetic Spectrum

Portrait of Sir William Herschel, pictured with the experiment that enabled him to discover infrared light. (Credit: NASA/IPAC)

How do you discover light that your eyes can't see? Serendipity. In the year 1800, Sir William Herschel was exploring the question of how much heat was contained by the different colors of visible light. He devised and experiment where he used a glass prism to separate sunlight into it's rainbow of colors. Then, he placed a thermometer under each color, with one extra thermometer just beyond the red light of the spectrum. He found that the thermometer that was seemingly out of the light had the highest temperature. Thus, he discovered infrared light.

A year later, Johann Wilhelm Ritter was inspired by Herschel's discovery to see if there might be light just beyond the purple end of the spectrum. Indeed, there was, and Ritter discovered ultraviolet light. In 1867, James Clerk Maxwell predicted that there should be light with even longer wavelengths than infrared light. In 1887 Heinrich Hertz demonstrated the existence of the waves predicted by Maxwell by producing radio waves in his laboratory.

It took a bit longer for scientists to discover the higher-energy (shorter wavelength) light in the electromagnetic spectrum.

Left: Portrait of Wilhelm Conrad Röntgen who is credited with discovering X-rays. Right: Mrs. Röntgen's hand, the first X-ray picture of the human body ever taken.

X-rays were first observed and documented in 1895 by Wilhelm Conrad Röntgen, a German scientist who found them quite by accident when experimenting with vacuum tubes. A week after he first observed them, he took an X-ray photograph of his wife's hand, which clearly revealed her wedding ring and her bones. The photograph electrified the general public and aroused great scientific interest in the new form of radiation . Röntgen called it "X" to indicate it was an unknown type of radiation. The name stuck, although many of his colleagues suggested calling them Röntgen rays.

While Röntgen first observed the effects of X-rays in 1895, it wasn't until 1912 that scientists were able to conclude that they were, indeed, another form of light."

Gamma-rays were first observed in 1900 by Paul Villard when he was investigating radiation from radium. A few years later, Ernest Rutherford proposed the name "gamma-rays," for this new radiation, and the name stuck. Like X-rays, the exact nature of gamma-rays took a little while for scientists to work out. In 1914, when Rutherford observed that they could be reflected off the layers of a crystal, it was clear that they were akin to X-rays (in other words another form of light), but with much shorter wavelengths.

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Hertz’s Experiments on Electromagnetic Waves

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• Salvo D’Agostino 5  

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 213))

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Heinrich Hertz’s decision to go to Helmholtz and to work in his laboratory in Berlin had great significance for his career in research. Helmholtz’s general outlook on science and physics had an initial bearing on Hertz’s own.

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For details of Hertz’s life, see “Hertz, Heinrich Rudolf”, in: McCormmach [1971] Vol. 6, 340–349. Hertz’s scientific formation is studied by Buchwald [1992], “The Training of German Research Physicist Heinrich Hertz”, in: Nye, Richard and Stuwer [1992].

Google Scholar  

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Hertz [1896] 3.

Hertz [1896] 33.

Hertz [1896] 34.

Helmholtz’s Preface to Hertz [1956] xxviii.

Hertz [1962] Introduction, “Theoretical” 23–26.

Hertz [1962] 1.

Hertz [1962] 2.

“Im Laboratorium die Arbeit begonnen über schnelle Schwingungen”. Note for 7 September 1887, in: Hertz Johanna [1928] 175.

Heinrich Hertz, “On the Relations between Maxwell’s Fundamental Electromagnetic Equations and the Fundamental Equations of the Opposing Electromagnetics”, in Hertz [1884]; Hertz [1896] 273–290.

According to Doncel (Doncel [1991]), these conclusions were not included in the Academy report and were added by Hertz on 17 February 1888, to the paper published in Wiedemann Annalen

Hertz [1962] 123, Paper No. 7, Conclusions.

Hertz [1962] 2. Concerning the further development of his experiments, Hertz maintained that “in altering the conditions I came upon the phenomenon of side sparks [secondary sparks] which formed the starting point of the following research”.

Hertz, “On Very Rapid Electric Oscillations”, in: Hertz (1962) 29–54, 29.

Hertz (1962] 33.

Hertz, “On Very Rapid Electric Oscllations”,in: Hertz [1962] 29–53, 42–43.

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Henri Poincarè, Comptes Rendus , 3 [1891], 322.

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Hertz, “Introduction, A) Experimental”, in: Hertz [1962] 4–5.

Hertz, “On the Action of a Rectilinear Electric Oscllation Upon a Neighbouring Circuit”, Wiedemann’s Annalen . 34 [1888], 155; reprinted in: Hertz [1962] 80–94.

Hertz [1962] 82–83.

Hertz [1962] 90–91.

Hertz [1962] 86–91.

Poincarè disagreed with Hertz’s interpretation of nodes: letter from Poincarè to Hertz, 11 September 1890 (Hertz’s Correspondence, Deutsches Museum, MS. 3000).; A. Righi maintained that the gap corresponded to an antinode, and modern theories would not accept either Hertz’s or Righi’s extreme positions.

Lodge [1894] 8–9.

Hertz, “On Electromagnetic Effects Produced by Electrical Disturbances in Insulators”, Sitzungsber . d. Berl. Akad. d. Wiss. (10 Novembre 1887); in Wiedemann’s Annalen , 34 [1888], 273; reprinted in: Hertz [1962] 95–106.

Hertz [1962] 96. D’Agostino [1976] 305.

Hertz [1962] 101.

A detailed interpretation of Hertz’s Academy Experiment in: Buchwald[1994] 254–261.

Hertz, “On the Finite Velocity of Propagation of Electromagnetic Actions”, presented at the Berlin Academy on 2 February 1888;reprinted in: Hertz [1962] 107–123.

Hertz [1962] 107.

Hertz [1962] 108.

Hertz [1962] 121. Hertz [1962] 151.

Hertz [1962] 121.

Hertz, “On Electromagnetic Waves in Air and Their Reflection.” Wiedemann’s Annalen , 34 [1888], 610; reprinted in: Hertz [1962] 124–136.

Hertz[1962] 133.

Hertz, “The Forces of Electric Oscillations, Treated According to Maxwell’s Theory”, Wiedemann’s Annalen , 36 [1889], 1; reprinted in: Hertz [1962] 137–159.

Hertz[1962] 140.

Hertz, Wiedemann’s Annalen , 36 [188]), 1; reprinted in: Hertz [1962 150.

Hertz [1962] 151.

Hertz [1962] 154.

Hertz [1962] 156.

Hertz[1962] 159.

Hertz[1962] 146.

Hertz [1962] 146; D’Agostino [1976] 318.

Hertz, “On the Propagation of Electric Waves by Means of Wires”, in: Hertz [1962] 160–171.

Heinrich Hertz, “On the Mechanical Action of Electric Waves in Wires”, Wiedemann’s Annalen , 42 (1891), 407; reprinted in: Hertz [1962] 186–194.

Hertz [1962] 160–161.

Hertz, “On Electric Radiation”, Sitzungsber. d. Berl. Akad. d. Wiss. (13 December 1888); in Wiedemann’s Annalen , 36 [1889], 769; reprinted in: Hertz [1962] 172–185.

Hertz[1962] 182–183.

Hertz [1962]124–136, 124.

Hertz[1962] 136.

Hertz, “On the Fundamental Equations of Electromagnetism for Bodies at Rest”, in: Hertz [1962] 195–241, 236.

Hertz “Introduction” 1–28, B) Theoretical, in: Hertz [1962] 22.

Hertz, “Introduction, A) Experimental”, in: Hertz [1962]. 6.

Hertz, “Introduction, A) Experimental”, in: Hertz [1962] 7.

Hertz [1962] 195.

Hertz “On the Fundamental Equations of Electromagnetism for Bodies at Rest”, Hertz [1962] 199 ff.

On Helmholtz’s polarisation: Helmholtz [187]) 615–618; Helmholtz [1881]. See also papers XXXII–XLI, in: Helmholtz [1882].

Hertz, “On the Fundamental Equations of Electromagnetism for Bodies at Rest”, in: Hertz [1962] 195–241 Section 4; especially “Isotropic Non Conductors”, 202 ff.

Helmholtz [1881] 818 ff. Hertz [1962], Introduction, 25.

Hertz [1962] 25.

Cazenobe [1980] refers to polarisation theories in his analysis of Hertz’s approach to the decisive experiment. Hertz’s and Helmholtz’s PT are estensively examined in: Buchwald [1994] 375–388.

According to accurate dating in a recent essay (Doncel [1991]), the majority of this paper was written shortly before 21 January 1888.

Helmholtz [1870] 573, 577, 625, 627.

Hertz [1962], 107; paper no. 7, dated: “February 1888.

Hertz, Introduction, in: Hertz [1962] 6.

I remarked this omission in 1975 (D’Agostino [1975] 310, 311).

Hertz [1962] Introduction 7.

Concerning this point, I disagree with Buchwald’s thesis (Buchwald [1994] 262–266) on the point that Hertz awaringly changed his 1888 logic in his 1892 Introduction (See D’Agostino “Hertz’s View on the Methods of Physics: Experiment and Theory Reconciled?” in: Baird, Hughes & Nordmann [1998] 89–102.

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D’Agostino, S. (2000). Hertz’s Experiments on Electromagnetic Waves. In: A History of the Ideas of Theoretical Physics. Boston Studies in the Philosophy of Science, vol 213. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9034-6_6

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16.1 Maxwell’s Equations and Electromagnetic Waves

Learning objectives.

By the end of this section, you will be able to:

• Explain Maxwell’s correction of Ampère’s law by including the displacement current
• State and apply Maxwell’s equations in integral form
• Describe how the symmetry between changing electric and changing magnetic fields explains Maxwell’s prediction of electromagnetic waves
• Describe how Hertz confirmed Maxwell’s prediction of electromagnetic waves

James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century ( Figure 16.2 ). Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to the nature of Saturn’s rings. He is probably best known for having combined existing knowledge of the laws of electricity and of magnetism with insights of his own into a complete overarching electromagnetic theory, represented by Maxwell’s equations .

Maxwell’s Correction to the Laws of Electricity and Magnetism

The four basic laws of electricity and magnetism had been discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday. Maxwell discovered logical inconsistencies in these earlier results and identified the incompleteness of Ampère’s law as their cause.

Recall that according to Ampère’s law, the integral of the magnetic field around a closed loop C is proportional to the current I passing through any surface whose boundary is loop C itself:

There are infinitely many surfaces that can be attached to any loop, and Ampère’s law stated in Equation 16.1 is independent of the choice of surface.

Consider the set-up in Figure 16.3 . A source of emf is abruptly connected across a parallel-plate capacitor so that a time-dependent current I develops in the wire. Suppose we apply Ampère’s law to loop C shown at a time before the capacitor is fully charged, so that I ≠ 0 I ≠ 0 . Surface S 1 S 1 gives a nonzero value for the enclosed current I , whereas surface S 2 S 2 gives zero for the enclosed current because no current passes through it:

Clearly, Ampère’s law in its usual form does not work here. This is an internal contradiction in the theory which requires a modification to the theory, Ampère’s law, itself.

How can Ampère’s law be modified so that it works in all situations? Maxwell suggested including an additional contribution, called the displacement current I d I d , to the real current I ,

where the displacement current is defined to be

Here ε 0 ε 0 is the permittivity of free space and Φ E Φ E is the electric flux , defined as

The displacement current is analogous to a real current in Ampère’s law, entering into Ampère’s law in the same way. It is produced, however, by a changing electric field. It accounts for a changing electric field producing a magnetic field, just as a real current does, but the displacement current can produce a magnetic field even where no real current is present. When this extra term is included, the modified Ampère’s law equation becomes

and is independent of the surface S through which the current I is measured.

We can now examine this modified version of Ampère’s law to confirm that it holds independent of whether the surface S 1 S 1 or the surface S 2 S 2 in Figure 16.3 is chosen. The electric field E → E → corresponding to the flux Φ E Φ E in Equation 16.3 is between the capacitor plates. Therefore, the E → E → field and the displacement current through the surface S 1 S 1 are both zero, and Equation 16.2 takes the form

We must now show that for surface S 2 , S 2 , through which no actual current flows, the displacement current leads to the same value μ 0 I μ 0 I for the right side of the Ampère’s law equation. For surface S 2 , S 2 , the equation becomes

Gauss’s law for electric charge requires a closed surface and cannot ordinarily be applied to a surface like S 1 S 1 alone or S 2 S 2 alone. But the two surfaces S 1 S 1 and S 2 S 2 form a closed surface in Figure 16.3 and can be used in Gauss’s law. Because the electric field is zero on S 1 S 1 , the flux contribution through S 1 S 1 is zero. This gives us

Therefore, we can replace the integral over S 2 S 2 in Equation 16.6 with the closed Gaussian surface S 1 + S 2 S 1 + S 2 and apply Gauss’s law to obtain

Thus, the modified Ampère’s law equation is the same using surface S 2 , S 2 , where the right-hand side results from the displacement current, as it is for the surface S 1 , S 1 , where the contribution comes from the actual flow of electric charge.

Example 16.1

Displacement current in a charging capacitor.

• The voltage between the plates at time t is given by V C = 1 C Q ( t ) = V 0 ( 1 − e − t / R C ) . V C = 1 C Q ( t ) = V 0 ( 1 − e − t / R C ) . Let the z -axis point from the positive plate to the negative plate. Then the z -component of the electric field between the plates as a function of time t is E z ( t ) = V 0 d ( 1 − e − t / R C ) . E z ( t ) = V 0 d ( 1 − e − t / R C ) . Therefore, the z-component of the displacement current I d I d between the plates is I d ( t ) = ε 0 A ∂ E z ( t ) ∂ t = ε 0 A V 0 d × 1 R C e − t / R C = V 0 R e − t / R C , I d ( t ) = ε 0 A ∂ E z ( t ) ∂ t = ε 0 A V 0 d × 1 R C e − t / R C = V 0 R e − t / R C , where we have used C = ε 0 A d C = ε 0 A d for the capacitance.
• From the expression for V C , V C , the charge on the capacitor is Q ( t ) = C V C = C V 0 ( 1 − e − t / R C ) . Q ( t ) = C V C = C V 0 ( 1 − e − t / R C ) . The current into the capacitor after the circuit is closed, is therefore I = d Q d t = V 0 R e − t / R C . I = d Q d t = V 0 R e − t / R C . This current is the same as I d I d found in (a).

Maxwell’s Equations

With the correction for the displacement current, Maxwell’s equations take the form

Once the fields have been calculated using these four equations, the Lorentz force equation

gives the force that the fields exert on a particle with charge q moving with velocity v → v → . The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. The magnetic and electric forces have been examined in earlier modules. These four Maxwell’s equations are, respectively,

1. Gauss’s law

The electric flux through any closed surface is equal to the electric charge Q in Q in enclosed by the surface. Gauss’s law [ Equation 16.8 ] describes the relation between an electric charge and the electric field it produces. This is often pictured in terms of electric field lines originating from positive charges and terminating on negative charges, and indicating the direction of the electric field at each point in space.

2. Gauss’s law for magnetism

The magnetic field flux through any closed surface is zero [ Equation 16.9 ]. This is equivalent to the statement that magnetic field lines are continuous, having no beginning or end. Any magnetic field line entering the region enclosed by the surface must also leave it. No magnetic monopoles, where magnetic field lines would terminate, are known to exist (see Magnetic Fields and Lines ).

3. Faraday’s law

A changing magnetic field induces an electromotive force (emf) and, hence, an electric field. The direction of the emf opposes the change. This third of Maxwell’s equations, Equation 16.10 , is Faraday’s law of induction and includes Lenz’s law. The electric field from a changing magnetic field has field lines that form closed loops, without any beginning or end.

4. Ampère-Maxwell law

Magnetic fields are generated by moving charges or by changing electric fields. This fourth of Maxwell’s equations, Equation 16.11 , encompasses Ampère’s law and adds another source of magnetic fields, namely changing electric fields.

Maxwell’s equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be immediately apparent. Faraday’s law describes how changing magnetic fields produce electric fields. The displacement current introduced by Maxwell results instead from a changing electric field and accounts for a changing electric field producing a magnetic field. The equations for the effects of both changing electric fields and changing magnetic fields differ in form only where the absence of magnetic monopoles leads to missing terms. This symmetry between the effects of changing magnetic and electric fields is essential in explaining the nature of electromagnetic waves.

Later application of Einstein’s theory of relativity to Maxwell’s complete and symmetric theory showed that electric and magnetic forces are not separate but are different manifestations of the same thing—the electromagnetic force. The electromagnetic force and weak nuclear force are similarly unified as the electroweak force. This unification of forces has been one motivation for attempts to unify all of the four basic forces in nature—the gravitational, electrical, strong, and weak nuclear forces (see Particle Physics and Cosmology ).

The Mechanism of Electromagnetic Wave Propagation

To see how the symmetry introduced by Maxwell accounts for the existence of combined electric and magnetic waves that propagate through space, imagine a time-varying magnetic field B → 0 ( t ) B → 0 ( t ) produced by the high-frequency alternating current seen in Figure 16.4 . We represent B → 0 ( t ) B → 0 ( t ) in the diagram by one of its field lines. From Faraday’s law, the changing magnetic field through a surface induces a time-varying electric field E → 0 ( t ) E → 0 ( t ) at the boundary of that surface. The displacement current source for the electric field, like the Faraday’s law source for the magnetic field, produces only closed loops of field lines, because of the mathematical symmetry involved in the equations for the induced electric and induced magnetic fields. A field line representation of E → 0 ( t ) E → 0 ( t ) is shown. In turn, the changing electric field E → 0 ( t ) E → 0 ( t ) creates a magnetic field B → 1 ( t ) B → 1 ( t ) according to the modified Ampère’s law. This changing field induces E → 1 ( t ) , E → 1 ( t ) , which induces B → 2 ( t ) , B → 2 ( t ) , and so on. We then have a self-continuing process that leads to the creation of time-varying electric and magnetic fields in regions farther and farther away from O . This process may be visualized as the propagation of an electromagnetic wave through space.

In the next section, we show in more precise mathematical terms how Maxwell’s equations lead to the prediction of electromagnetic waves that can travel through space without a material medium, implying a speed of electromagnetic waves equal to the speed of light.

Prior to Maxwell’s work, experiments had already indicated that light was a wave phenomenon, although the nature of the waves was yet unknown. In 1801, Thomas Young (1773–1829) showed that when a light beam was separated by two narrow slits and then recombined, a pattern made up of bright and dark fringes was formed on a screen. Young explained this behavior by assuming that light was composed of waves that added constructively at some points and destructively at others (see Interference ). Subsequently, Jean Foucault (1819–1868), with measurements of the speed of light in various media, and Augustin Fresnel (1788–1827), with detailed experiments involving interference and diffraction of light, provided further conclusive evidence that light was a wave. So, light was known to be a wave, and Maxwell had predicted the existence of electromagnetic waves that traveled at the speed of light. The conclusion seemed inescapable: Light must be a form of electromagnetic radiation. But Maxwell’s theory showed that other wavelengths and frequencies than those of light were possible for electromagnetic waves. He showed that electromagnetic radiation with the same fundamental properties as visible light should exist at any frequency. It remained for others to test, and confirm, this prediction.

Check Your Understanding 16.1

When the emf across a capacitor is turned on and the capacitor is allowed to charge, when does the magnetic field induced by the displacement current have the greatest magnitude?

Hertz’s Observations

The German physicist Heinrich Hertz (1857–1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. Starting in 1887, he performed a series of experiments that not only confirmed the existence of electromagnetic waves but also verified that they travel at the speed of light.

Hertz used an alternating-current RLC (resistor-inductor-capacitor) circuit that resonates at a known frequency f 0 = 1 2 π L C f 0 = 1 2 π L C and connected it to a loop of wire, as shown in Figure 16.5 . High voltages induced across the gap in the loop produced sparks that were visible evidence of the current in the circuit and helped generate electromagnetic waves.

Across the laboratory, Hertz placed another loop attached to another RLC circuit, which could be tuned (as the dial on a radio) to the same resonant frequency as the first and could thus be made to receive electromagnetic waves. This loop also had a gap across which sparks were generated, giving solid evidence that electromagnetic waves had been received.

Hertz also studied the reflection, refraction, and interference patterns of the electromagnetic waves he generated, confirming their wave character. He was able to determine the wavelengths from the interference patterns, and knowing their frequencies, he could calculate the propagation speed using the equation v = f λ v = f λ , where v is the speed of a wave, f is its frequency, and λ λ is its wavelength. Hertz was thus able to prove that electromagnetic waves travel at the speed of light. The SI unit for frequency, the hertz ( 1 Hz = 1 cycle/s 1 Hz = 1 cycle/s ), is named in his honor.

Check Your Understanding 16.2

Could a purely electric field propagate as a wave through a vacuum without a magnetic field? Justify your answer.

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Heinrich Hertz

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• Famous Scientists - Biography of Heinrich Hertz
• Magnet Academy - Biography of Heinrich Hertz
• Heinrich Hertz - Student Encyclopedia (Ages 11 and up)

Heinrich Hertz (born February 22, 1857, Hamburg [Germany]—died January 1, 1894, Bonn , Germany) was a German physicist who showed that Scottish physicist James Clerk Maxwell’s theory of electromagnetism was correct and that light and heat are electromagnetic radiations .

He received a Ph.D. magna cum laude from the University of Berlin in 1880, where he studied under Hermann von Helmholtz . In 1883 he began his studies of Maxwell’s electromagnetic theory. Between 1885 and 1889, while he was professor of physics at the Karlsruhe Polytechnic, he produced electromagnetic waves in the laboratory and measured their length and velocity . He showed that the nature of their vibration and their susceptibility to reflection and refraction were the same as those of light and heat waves. As a result, he established beyond any doubt that light and heat are electromagnetic radiations. The electromagnetic waves were called Hertzian and, later, radio waves. (He was not the first to produce such waves. Anglo-American inventor David Hughes had done so in work that was almost universally ignored in 1879, but Hertz was the first to correctly understand their electromagnetic nature.) In 1889 Hertz was appointed professor of physics at the University of Bonn, where he continued his research on the discharge of electricity in rarefied gases.

His scientific papers were translated into English and published in three volumes: Electric Waves (1893), Miscellaneous Papers (1896), and Principles of Mechanics (1899).

Electromagnetic waves

Experiments and demonstrations on the nature of electromagnetic waves.

The nature of electromagnetic waves is demonstrated first with the aid of models and then by a reconstruction of Faraday’s experiment on induction. The range of electromagnetic waves is illustrated next, followed by a series of experiments using a klystron. The measurement of wavelengths is then introduced by showing standing waves with the Vinycomb model. Bragg finally illustrates the same principles by applying electromagnetic waves to Young’s pinhole experiment.

Crown copyright information is reproduced with the permission of the Controller of HMSO and the Queen’s Printer for Scotland.

Browse Course Material

Course info.

• Prof. Yen-Jie Lee

Departments

As taught in.

• Atomic, Molecular, Optical Physics
• Classical Mechanics
• Electromagnetism

Learning Resource Types

Physics iii: vibrations and waves, part ii: electromagnetic waves.

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