Wilhelm Weber

How to use this course

Wilhelm Weber’s name is on the SI unit of magnetic flux, and most students meet him nowhere else. In his own century he was one of the leading physicists of Europe. With Carl Friedrich Gauss he made magnetism a science of absolute measurement and built one of the first working electromagnetic telegraphs. Alone, he built the instruments that turned electrical quantities into numbers, and he proposed the first unified law of electric and magnetic forces between moving charges. With Rudolf Kohlrausch he measured a constant in that law and found it close to the speed of light, the number James Clerk Maxwell would use to argue that light is an electromagnetic wave.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Formulas are given in SI units unless a lesson is explicitly about the old Gaussian systems. The lessons follow his work in order: absolute magnetic measurement (1832–1840), the telegraph and induction (1833–1837), the electrodynamometer and the force law (1846), the debate over energy (1847–1875), the ratio of units (1855–1857), and the electrical theory of matter (1852–1876).

Timeline

Wittenberg and Halle, 1804–1831

Wilhelm Eduard Weber was born in Wittenberg on 24 October 1804, one of many children of Michael Weber, professor of theology at the old university of Luther’s town. Three of the sons became distinguished scientists. Ernst Heinrich, nine years older, became a professor of anatomy and physiology at Leipzig and is remembered for the Weber law of perception. Eduard Friedrich, two years younger, became an anatomist and physiologist. Wilhelm worked with both.

The Napoleonic wars disrupted Wittenberg’s university, which was later merged into Halle’s. The family moved to Halle in 1814, where Wilhelm attended school and, from 1822, the university. His teacher was the physicist and chemist Johann Schweigger, who in 1820 had built the multiplier, the first galvanometer, by winding a wire many times around a compass needle.

Waves and organ pipes

As a student Weber experimented with his brother Ernst Heinrich on waves in water and other liquids, using a long glass-walled trough to watch the motion of particles as a wave passed. Their book Wellenlehre auf Experimente gegründet (Wave theory founded on experiments) appeared in 1825 and ran to nearly six hundred pages. It was a work of careful observation more than of theory, and it set the pattern of Weber’s career: the patient design of experiments that yield clean numbers.

His doctorate (1826) and his habilitation (1827) were on the theory of reed pipes in organs. He became Privatdozent in 1827 and extraordinary professor of natural philosophy at Halle in 1828. That year he attended the meeting of German scientists and physicians in Berlin organized by Alexander von Humboldt. Gauss, staying with Humboldt, met him there and noticed his work.

Göttingen with Gauss, 1831–1837

In 1831 the chair of physics at Göttingen fell vacant on the death of Tobias Mayer the younger. Gauss recommended Weber, who accepted in April and took up the post at the age of 26. The partnership with Gauss, twenty-seven years older, was one of the most productive in the history of physics. Gauss brought mathematical power and the habits of precise astronomy; Weber brought experimental skill and inexhaustible ingenuity with apparatus. Weber also opened the physics laboratory to students, who could experiment there free of charge.

Their first subject was the Earth’s magnetism. In 1832 Gauss showed how to measure the horizontal intensity of the Earth’s field in units of length, mass and time, independently of any particular magnet (Lesson 04). They then needed to compare measurements made at the same moment at different places, which led to a network of observatories, the Göttingen Magnetic Union, founded in 1836 with the support of Humboldt. Its observers read their instruments at agreed times across Europe, and Gauss and Weber edited the results in six volumes from 1837 to 1843.

The telegraph

In 1833 Gauss and Weber strung a double wire over the roofs of Göttingen between the observatory and the physics institute, about a kilometre apart, and used it to send signals by the deflections of a magnetized bar. They are said to have exchanged the message Michelmann kommt (Michelmann is coming), Michelmann being the institute’s attendant, though the story is unverified. They understood the commercial possibilities but had no means to exploit them, and the line served mainly for scientific work. Lesson 05 explains how it worked.

In 1836 Weber and his brother Eduard published Mechanik der menschlichen Gehwerkzeuge (Mechanics of the human walking apparatus), a pioneering study of human locomotion. In 1837 Weber invented the earth inductor, a coil rotated in the Earth’s field to measure it by induction.

The Göttingen Seven and Leipzig, 1837–1849

On the death of William IV in June 1837, the crowns of Britain and Hanover separated. Hanover passed to William’s brother Ernst August, who in November revoked the liberal constitution granted in 1833. Seven Göttingen professors signed a formal protest declaring that they remained bound by their oath to the constitution. Among them were the brothers Jacob and Wilhelm Grimm, the historian Friedrich Dahlmann, the orientalist Heinrich Ewald, husband of Gauss’s daughter Wilhelmine, and Weber, the only natural scientist of the group. On 14 December 1837 all seven were dismissed. Three were also expelled from the kingdom. Weber was not, but he refused to retract and lost his salary.

Gauss, conservative by temperament, did not join the protest and could not reverse the dismissals. Weber stayed in Göttingen as a private scholar for several years, continuing the magnetic work with Gauss: the Resultate and the Atlas des Erdmagnetismus (1840), prepared with Gauss and Carl Wolfgang Benjamin Goldschmidt, date from these years. Between March and August 1838 he travelled to Berlin, London and Paris; in London he spoke with John Herschel among others. Göttingen filled the physics chair in 1839 with Johann Benedict Listing.

In 1843 Weber accepted the chair of physics at Leipzig, succeeding Gustav Theodor Fechner, who had retired because of an eye illness. His brothers Ernst Heinrich and Eduard were already there. At Leipzig he completed the instrument that tested Ampère’s law, the electrodynamometer, and published his fundamental law of electrical action in 1846, in the first memoir of the series Elektrodynamische Maassbestimmungen (Electrodynamic measurements). That year he was elected to the new Saxon Academy of Sciences, in whose transactions the series appeared. After the revolution of 1848 the Hanoverian government restored him, and in 1849 he returned to Göttingen. He insisted that Listing keep the chair he had held since 1839.

Absolute units: weighing a magnetic field

For the general reader. Before 1832 a magnetic field could only be compared with another field, using a particular needle whose strength was unknown and changed over time. Gauss, with Weber’s help, found how to express the Earth’s field in the same units as mass, length and time, using two experiments with two magnets. Weber then applied the same idea to electric currents, charges and resistances. The modern SI and its electrical units descend from this programme.

Two experiments

Let a bar magnet of magnetic moment \(m\) and moment of inertia \(J\) hang horizontally. In the horizontal component \(B_H\) of the Earth’s field, small oscillations about the meridian have period

\(J\) can be found from the magnet’s mass and shape, or by adding known masses and timing again. Then the same magnet is laid on the east–west line, at distance \(r\) from a small auxiliary needle. The magnet’s field at the needle is perpendicular to \(B_H\) and deflects it by \(\theta\).

In the first position the needle deflects by \(\tan\theta=\frac{\mu_0}{4\pi}\frac{2m}{r^3B_H}\), which measures \(m/B_H\). Combining with the oscillations:

The unknown moment \(m\) cancels. In practice the deflection is measured at two distances \(r_1,r_2\) to eliminate the next term of the multipole expansion, of order \(r^{-5}\). Gauss used millimetre, milligram and second as base units, and Weber’s electrical units were built the same way. In the Gaussian system, where \(\mu_0/4\pi\) is replaced by 1, this gives \(B_H\) in gauss.

Bifilar suspension

Weber hung heavy magnets and coils from two parallel threads instead of one. If threads of length \(\ell\), a distance \(2a\) apart, carry a weight \(Mg\), turning the load by a small angle \(\varphi\) raises it slightly, and the restoring torque is \(\tau=\dfrac{Mga^2}{\ell}\sin\varphi\). The constant is fixed by the geometry and the weight alone, so torques can be measured absolutely, and it is far stiffer than the torsion of a single thread. Bifilar magnetometers measured variations in the Earth’s field at the Magnetic Union stations, and the electrodynamometer of Lesson 06 hangs the same way.

Induction, the telegraph and the earth inductor

For the general reader. In 1831 Michael Faraday discovered that a changing magnetic field drives a current in a coil. Two years later Gauss and Weber used both halves of electromagnetism to send messages. Pulses of current, at first from batteries and soon from a coil moved past a magnet, travelled a kilometre of wire and twisted a magnet hanging from a thread. A tiny mirror and a telescope made the twist visible. Weber then turned induction into a measuring tool, the earth inductor.

Pulses of charge

This is why induction suits signalling and measurement. The operator need not move the coil at a controlled speed: each push sends the same charge. Reversing the direction of motion reverses the pulse, so a receiver can distinguish two symbols.

The receiver

A short pulse of charge \(Q\) through a coil surrounding a suspended magnet gives the magnet an angular impulse proportional to \(Q\). If the pulse is short compared with the period \(T\) of free oscillation, the magnet swings out to a first maximum \(\theta_{\max}\) proportional to \(Q\): this is the ballistic galvanometer. The deflections in the telegraph were small. Weber read them with a mirror fixed to the magnet: a telescope a few metres away viewed the reflection of a graduated scale, so that a rotation \(\theta\) of the mirror shifted the image by \(2D\theta\) at distance \(D\). The method, which Gauss introduced for his magnetometer, became standard for sensitive galvanometers. Letters were coded by short combinations of deflections in the two directions. At first the current came from batteries; induction coils moved over magnets later replaced them.

The earth inductor

Weber’s earth inductor of 1837 is a large coil that can be turned through \(180^\circ\) about an axis. Turned about a vertical axis, starting with its plane perpendicular to the meridian, it sends through a ballistic galvanometer a charge \(Q_H=2NAB_H/R\). Turned about a horizontal axis lying in the meridian, starting horizontal, it sends \(Q_V=2NAB_V/R\). Then

where \(I\) is the magnetic inclination (dip). The ratio needs no knowledge of \(N\), \(A\), \(R\) or the galvanometer constant. With them, the same instrument gives \(B_H\) and \(B_V\) separately in absolute units.

The electrodynamometer and Ampère’s law

For the general reader. André-Marie Ampère founded his theory of the force between currents on experiments in which forces cancel, because he could not measure them directly with any precision. Weber built an instrument that could. A small coil hangs from two threads inside a larger fixed coil. When current passes through both, the small coil turns, and the angle measures the product of the two currents. With this electrodynamometer Weber confirmed Ampère’s law with far greater precision than Ampère had achieved.

Torque between coils

Let a fixed coil carry current \(I_1\) and a movable coil, turned by angle \(\varphi\), carry \(I_2\). Their mutual inductance \(M(\varphi)\) depends on the angle. The magnetic energy available to do work is \(I_1I_2M(\varphi)\) at fixed currents, so

Weber placed the coils at right angles at rest, \(\varphi=0\), where the torque is greatest, and balanced it with the bifilar suspension of Lesson 04. When the same current passes through both coils in series, \(\tau\propto I^2\): the deflection does not change sign when the current reverses. The instrument therefore measures the mean square of an alternating current, and its descendants, the electrodynamic ammeters and wattmeters, were used in alternating-current engineering for a century.

Testing Ampère’s law

Weber used the electrodynamometer to check the predictions of Ampère’s law for coils at different distances and orientations. Because the instrument gave numbers, not only null results, he could compare its readings with the forces computed from Ampère’s formula. Within his accuracy the agreement was complete. In the same 1846 memoir he went further and asked what law between moving charges would produce Ampère’s law between current elements, and Faraday’s induction as well. Lesson 07 gives his answer.

Weber’s force law

For the general reader. Newton’s gravity acts between two masses and depends only on how far apart they are. Coulomb found the same for electric charges at rest. Weber proposed in 1846 that charges in motion attract or repel each other with a force that also depends on how fast, and how quickly, their distance changes. From this one law he derived the electrostatic force, Ampère’s force between currents and Faraday’s induction. It was the first unified theory of electricity and magnetism.

The law

Gauss had considered in 1835 a force between charges depending on their relative velocity, but did not publish it. Weber’s law, from the 1846 memoir, reads:

Weber wrote the constant as \(4/a\) and determined \(c_W\) with Kohlrausch only later (Lesson 09). Note the kinematics: if \(\mathbf r\) is the relative position and \(\mathbf u=\dot{\mathbf r}\) the relative velocity, then

From charges to currents

Weber adopted Fechner’s hypothesis: a current element \(I\,d\mathbf s\) consists of equal positive and negative charges \(\pm e\) moving in opposite directions with velocities \(\pm\mathbf v\), so that \(I\,d\mathbf s=2e\mathbf v\) and the element is neutral.

Proof. With \(\dot{\mathbf u}=0\), the bracket in Weber’s law for a pair with relative velocity \(\mathbf u\) is \(1+\frac{u^2}{c^2}-\frac{3}{2}\frac{(\hat{\mathbf r}\cdot\mathbf u)^2}{c^2}\). There are four pairs:

The constant terms cancel: the elements are neutral. Since \(|\mathbf v_1-\mathbf v_2|^2-|\mathbf v_1+\mathbf v_2|^2=-4\,\mathbf v_1\cdot\mathbf v_2\), the \(u^2\) terms sum to \(-8e_1e_2\,\mathbf v_1\cdot\mathbf v_2/c^2\), and likewise the \((\hat{\mathbf r}\cdot\mathbf u)^2\) terms sum to \(-8e_1e_2(\hat{\mathbf r}\cdot\mathbf v_1)(\hat{\mathbf r}\cdot\mathbf v_2)/c^2\). The total is

Substitute \(e_i\mathbf v_i=\tfrac12I_id\mathbf s_i\) and \(1/(\varepsilon_0c^2)=\mu_0\). \(\square\)

Induction

The acceleration term \(r\ddot r/c^2\) does not cancel when a current changes: positive and negative charges then accelerate in opposite directions, and the force on the charges of a nearby conductor differs for the two signs. It pushes them apart along the wire, driving a current. Weber showed that this reproduces the laws of induction found by Faraday and formulated by Franz Neumann, both for changing currents and for moving circuits. For the first time one formula covered Coulomb, Ampère and Faraday.

Energy, potential and Helmholtz’s objection

For the general reader. In 1847 Hermann von Helmholtz argued that energy is conserved only if forces depend on distance alone. Weber’s force depends on velocity and acceleration, so Helmholtz concluded at first that it violates the conservation of energy. Weber replied by exhibiting an energy function that his law conserves. Helmholtz then changed his attack, arguing that the law allows charges to behave as if they had negative mass. The debate ran for some thirty years and ended only with the victory of field theory.

Conservation of energy

Proof. The force on particle 1 is \(F\hat{\mathbf r}\) and on particle 2 is \(-F\hat{\mathbf r}\), so the kinetic energy changes at the rate \(F\hat{\mathbf r}\cdot(\mathbf v_1-\mathbf v_2)=F\dot r\). Let \(k=ee'/4\pi\varepsilon_0\) and \(W=\frac kr\big(1-\frac{\dot r^2}{2c^2}\big)\). Then

So \(\frac{d}{dt}(\text{kinetic}+W)=0\). \(\square\)

The force can also be derived from the Lagrangian \(L=\tfrac12m_1v_1^2+\tfrac12m_2v_2^2-U\) with the velocity-dependent potential \(U=\frac kr\big(1+\frac{\dot r^2}{2c^2}\big)\). The sign of the velocity term differs from that in \(W\), as it must: the energy is \(\sum\dot q\,\partial L/\partial\dot q-L\), and the velocity term in \(U\) changes sign under this operation (Exercise 8.1). Weber’s law was in fact one of the first examples of a velocity-dependent potential.

Negative mass

In the 1870s Helmholtz argued that Weber’s law leads to physically absurd motions. The simplest version: a charge inside a charged spherical shell feels a force proportional to its own acceleration.

Proof. An element \(dQ=Q\,d\Omega/4\pi\) at \(R\hat{\mathbf n}\) has \(\hat{\mathbf r}=-\hat{\mathbf n}\) (from the element to the charge), \(\dot r=-\hat{\mathbf n}\cdot\mathbf v\) and \(\ddot r=\frac{v^2-(\hat{\mathbf n}\cdot\mathbf v)^2}{R}-\hat{\mathbf n}\cdot\mathbf a\). Every term of the bracket that is even in \(\hat{\mathbf n}\), multiplied by \(-\hat{\mathbf n}\), integrates to zero over the sphere. What remains is \(\frac{kq\,dQ}{R^2}\cdot\frac{R}{c^2}(\hat{\mathbf n}\cdot\mathbf a)\hat{\mathbf n}\), and \(\int\hat{\mathbf n}\hat{\mathbf n}\,d\Omega/4\pi=\tfrac13 I\). Hence \(\mathbf F=\frac{qQ}{4\pi\varepsilon_0}\frac{\mathbf a}{3Rc^2}=\frac{\mu_0qQ}{12\pi R}\mathbf a\). \(\square\)

For like charges and a large enough \(Q/R\), the effective mass is negative, and a charge pushed one way accelerates the other way, gaining kinetic energy without limit. Weber and his defenders replied that the required charges are unattainably large; Helmholtz replied that a fundamental law should not need such a rescue. Maxwell, who admired Weber’s work, nevertheless preferred to put the energy in the field.

The ratio of units and the speed of light

For the general reader. An electric charge can be measured in two ways: by the force it exerts at rest on another charge, or by the magnetic effect it produces when it flows through a wire. Each gives a unit of charge, and the ratio between the two units is a speed. In 1855–56 Weber and Rudolf Kohlrausch measured it by charging a Leyden jar, weighing the charge electrically, and then discharging it through a galvanometer. They found a speed very close to that of light. Maxwell soon argued that this was no coincidence.

Two units of charge

In the electrostatic system, the unit charge repels an equal charge at unit distance with unit force: \(F=q_s^2/r^2\). In the electromagnetic system, the unit current is defined by the force between currents, and the unit charge is the charge carried by unit current in unit time. Comparing the force between two charges with the force between two currents shows that \(q_s/q_m\) has the dimension of length over time.

In SI terms the experiment measures \(\varepsilon_0\) given \(\mu_0\), or vice versa. A charge \(Q\) produces an electrostatic force \(Q^2/(4\pi\varepsilon_0r^2)\) and, through a galvanometer of known constant, a magnetic throw determined by \(\mu_0Q\). Measuring both for the same \(Q\) yields \(\varepsilon_0\mu_0=1/c^2\).

The experiment

Weber and Kohlrausch charged a Leyden jar and measured the charge on it by sharing it with a sphere and measuring the electrostatic force with a torsion balance. They then discharged the jar through a ballistic galvanometer with a multiplier of 5635 windings and read the first throw of the magnet with mirror and scale. Comparing the throw with that produced by a known steady current for a known short time gave the charge in electromagnetic units. Their result, announced in 1855 and published in 1856 and in full in 1857, was

about 1.5 per cent below the value of roughly 315 000 km/s that Hippolyte Fizeau had found for the speed of light in 1849, and about 4 per cent above the modern value 299 792 km/s. The 1856 paper is often cited as the first to use the letter \(c\) for a constant of this kind; there it denoted Weber’s \(c_W\).

Kirchhoff and Maxwell

In 1857 Gustav Kirchhoff, working from Weber’s theory, derived the equations for a signal on a telegraph wire. In a wire of low resistance the signal travels at \(c_W/\sqrt2\), the speed of light. Weber reached the same result independently, in a longer analysis published in 1864. Neither concluded that light is electrical. In 1861–62 Maxwell computed the speed of transverse waves in his model of the ether from the Weber–Kohlrausch value, found it agreed with Fizeau’s speed of light, and inferred that light consists of transverse undulations of the same medium that causes electric and magnetic phenomena.

Molecular currents, diamagnetism and the electric atom

For the general reader. Weber believed that electricity consists of particles and that magnetism comes from particles circling inside molecules. In this picture iron is magnetic because its molecules are small magnets that line up. Bismuth and other diamagnetic materials are pushed away from magnets because a magnet induces currents in their molecules that oppose it. At the end of his life he proposed an atom made of a heavy charged core with light charges orbiting it. The electron, discovered six years after his death, made much of this picture look prophetic.

Rotating molecular magnets

Weber took Ampère’s molecular currents literally and supposed that each molecule of iron is a permanent magnet free to turn, held in place by forces from its neighbours. An applied field rotates them toward its direction; as all of them align, magnetization saturates. In this way he explained why magnetization does not grow without limit, and why some of it remains when the field is removed.

Diamagnetism by induction

Faraday discovered in 1845 that bismuth is repelled by a magnet. Weber explained the effect by induction in molecules containing closed circuits without resistance. When an external field is switched on, Faraday’s law drives a current in each circuit opposing the change of flux, and since there is no resistance the current persists.

Proof. With no resistance, the total flux through the ring is constant: \(LI+BA=0\). The moment is \(IA\). The energy is \(\tfrac12LI^2=\tfrac12B^2A^2/L\), which increases with \(B\); the force \(-\nabla\) of this energy points down the field gradient. \(\square\)

The modern explanation, due to Paul Langevin in 1905, replaces the rings by electron orbits whose motion is altered by the field while it is being switched on, and quantum mechanics later justified the absence of resistance. The structure of Weber’s argument survives.

The electric atom

In the Principien einer elektrodynamischen Theorie der Materie (1876) and in later memoirs, Weber proposed that ponderable matter is built from electrical particles. He supposed that an atom consists of a heavy charged particle around which light particles of opposite sign revolve, and that conduction consists in light particles moving from atom to atom. He used his force law, with its limiting speed, to discuss the stability of such orbits. Hendrik Lorentz’s electron theory of the 1890s combined discrete charges, as Weber had imagined them, with Maxwell’s fields.

Göttingen again, 1849–1891

Weber returned to Göttingen in 1849 and remained there for the rest of his life. He shared physics with Listing and led a seminar in mathematical physics that trained a generation. Bernhard Riemann worked as his assistant for about eighteen months around 1850 and took part in his experiments. Richard Dedekind attended the seminar from its start. Weber’s doctoral students included Ernst Abbe and Theodor Reye (both 1861), Friedrich Kohlrausch, Rudolf Kohlrausch’s son (1863), and Eduard Riecke (1871); Arthur Schuster and Gottlob Frege also studied with him. After Gauss’s death in 1855 he also took charge of the observatory for several years.

The Elektrodynamische Maassbestimmungen continued for three decades, seven memoirs in all between 1846 and 1878, on resistance measurement in absolute units, diamagnetism, the ratio of units, electrical oscillations (1864), and the energy of his law. The British Association’s committee on electrical standards, with William Thomson and Maxwell among its members, adopted the Gauss–Weber absolute method as the basis of its units in the early 1860s. From 1870 Weber defended his law against Helmholtz in a long and sometimes bitter exchange. Helmholtz’s 1881 proposal of the name ampere for the unit of current, rather than weber, was read by some as partly a product of that rivalry.

Honours came from every side. He became a Foreign Member of the Royal Society in 1850 and received its Copley Medal in 1859. He was elected to the Leopoldina in 1860 and received the Prussian Pour le Mérite for Sciences and Arts in 1864, the Matteucci Medal in 1879, and the title of privy councillor. He was director of the Göttingen Academy of Sciences from 1855 to 1885. He never married; his sister and later his niece kept his household. He died at his home in Göttingen on 23 June 1891, aged 86, and was buried in the city cemetery, where Max Planck and Max Born were later buried too.

Legacy: units, fields and particles

In 1899 Göttingen unveiled a monument to Gauss and Weber, showing the two men in conversation. The pairing is just. Their partnership made electricity and magnetism into sciences of measurement, and every electrical unit in use today descends from it.

• Units: the absolute system of electrical and magnetic units; the weber, the SI unit of magnetic flux, recommended by the International Electrotechnical Commission in 1935. \(1\ \mathrm{Wb}=1\ \mathrm{V\,s}\), the flux whose uniform decline to zero in one second induces one volt in a single turn.
• Instruments: the electrodynamometer, the earth inductor, the bifilar magnetometer, and mirror-and-scale reading of sensitive galvanometers.
• Communication: one of the first working electromagnetic telegraphs (1833).
• Theory: the first unified law of electric and magnetic forces; one of the first velocity-dependent potentials in mechanics; the measured constant that pointed Maxwell to the electromagnetic nature of light; the first detailed electrical picture of the atom.
• Honours: the lunar crater Weber; the Gauss–Weber Medal of the University of Göttingen.

Weber’s force law lost to Maxwell’s field theory once Heinrich Hertz detected electromagnetic waves, which a law of instantaneous action at a distance cannot describe. It has been studied again since the late twentieth century as a model of relational mechanics, and as a historical lesson in how two theories can agree on every closed circuit and still describe different worlds.

Connections

People linked to Wilhelm Weber across this collection. A name without a link has no page here yet. See Wilhelm Weber in the network of all 337 lives →

Teachers and advisors

• Johann Schweigger 1826

Students

• Bernhard Riemann
• Richard Dedekind
• Eduard Riecke 1871
• Ernst Abbe 1861
• Friedrich Kohlrausch 1863
• Theodor Reye 1861

Influenced by

• André-Marie Ampère
• Michael Faraday
• Gustav Theodor Fechner

Influenced

• David Hilbert
• Gottlob Frege
• Gustav Kirchhoff
• Heinrich Hertz
• Hermann Minkowski
• James Clerk Maxwell
• Teiji Takagi

Colleagues and collaborators

• Alexander von Humboldt
• Bernhard Riemann 1849-1866
• Carl Friedrich Gauss 1831-1855
• Leopold Kronecker
• Richard Dedekind 1876-1882
• Johann Benedict Listing 1849-1882
• Rudolf Kohlrausch 1854-1857

Rivals

• Hermann von Helmholtz 1847-1881

Family

• Eduard Friedrich Weber
• Ernst Heinrich Weber

Also mentioned in this life

• Jean-Baptiste Biot
• Niels Bohr
• Max Born
• Charles-Augustin de Coulomb
• Albert Einstein
• Leonhard Euler
• Hippolyte Fizeau
• John Herschel
• William Thomson, Lord Kelvin
• Joseph-Louis Lagrange
• Paul Langevin
• Hendrik Antoon Lorentz
• Isaac Newton
• Georg Simon Ohm
• Max Planck

Fields

• electromagnetism 12 lives
• geomagnetism 3 lives
• metrology 5 lives
• acoustics 9 lives

On CoursesHub

• Classical Electrodynamics

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, Wilhelm Weber, MacTutor History of Mathematics.
2. Wilhelm Eduard Weber, Wikipedia; and the German article.
3. Wilhelm Eduard Weber, Encyclopaedia Britannica.
4. National MagLab, Wilhelm Weber, Magnet Academy.
5. K. H. Wiederkehr, Wilhelm Eduard Weber: Erforscher der Wellenbewegung und der Elektrizität, Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1967.
6. K. Jungnickel and R. McCormmach, Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, vol. 1, University of Chicago Press, 1986.

Physics

1. W. Weber, Elektrodynamische Maassbestimmungen über ein allgemeines Grundgesetz der elektrischen Wirkung, Abhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften (1846). In Wilhelm Weber’s Werke, vol. 3, Springer, 1893.
2. R. Kohlrausch and W. Weber, Über die Elektricitätsmenge, welche bei galvanischen Strömen durch den Querschnitt der Kette fliesst, Annalen der Physik 99 (1856), 10–25.
3. A. K. T. Assis, On the first electromagnetic measurement of the velocity of light by Wilhelm Weber and Rudolf Kohlrausch (2003).
4. A. K. T. Assis, Weber’s Electrodynamics, Kluwer, 1994.
5. Weber electrodynamics, Wikipedia.
6. C. F. Gauss, Intensitas vis magneticae terrestris ad mensuram absolutam revocata, Göttingen, 1832/1833.
7. J. C. Maxwell, A Treatise on Electricity and Magnetism, Oxford, 1873, vol. 2, chapter 23 (on theories of action at a distance).
8. Weber (unit), Wikipedia.