Weber electrodynamics is only applicable for electrostatics, magnetostatics and for the quasistatic approximation.
Weber electrodynamics is not suitable for describing electromagnetic waves and for calculating the forces between electrically charged particles that move very rapidly or that are accelerated more than insignificantly.
Around 1820, André-Marie Ampère carried out numerous systematic experiments with direct currents.
In fact, today Ampere's force law is no longer presented in its original form, as there are equivalent representations for direct currents such as the Biot-Savart law in combination with the Lorentz force.
This is the point at which Weber electrodynamics and Maxwell electrodynamics take different paths, because James Clerk Maxwell decided to base his theory on the Biot-Savart law, which was originally also only valid for closed conductor loops.
Weber also carried out numerous experiments and documented the state of knowledge at this time in his substantial work.
[6][7][8] Weber electrodynamics and Gauss's hypothesis fell gradually into oblivion after the introduction of the displacement current around 1870, since the full set of Maxwell equations made it possible to describe electromagnetic waves for the first time.
From around 1880, experiments such as the Michelson-Morley experiment showed that electromagnetic waves propagate at the speed of light regardless of the state of motion of the transmitter or receiver in a vacuum, which is not consistent with the predictions of Maxwell's equations, since these describe wave propagation in a medium.
As a result, Gauss's hypothesis that the electric force depends on the relative velocity was added back in a modified form.
The conservation of energy in an isolated system consisting of only two particles is easy to demonstrate.
Except for the sign, the right-hand side corresponds to the time derivative of the kinetic energy.
As Maxwell already demonstrated around 150 years ago, under these conditions the Ampere force law can be represented in several variations.
[4] Maxwell's electrodynamics follows a two-stage approach, firstly by assigning a magnetic field
was interpreted as the velocity of the test charge relative to the medium in which the magnetic field propagates.
In Maxwell's electrodynamics, the Lorentz force is a physical law that cannot be traced back to a cause or mechanism.
Gauss's hypothesis of 1835 therefore already represents an early interpretation of magnetism as a relativistic effect.
For alternating currents and point charges, the different representations of Ampere's force law are not equivalent.
[11] Nevertheless, he decided to build his theory on the Biot-Savart law by generalizing it to cases where the conductor loops contain discontinuities.
The significance of the displacement current becomes clear by studying the field of the electromagnetic force that an accelerated electron would generate on a resting test charge.
The figures show the field of an electron that is accelerated to 75 percent of the speed of light within 3 nanoseconds.
In the case of the Weber force, it can be recognized that the initially radial field becomes flattened in the direction of motion.
[12] The well-known phenomenon of radiation pressure proves that electromagnetic waves are indeed able to "push" on matter.
, respectively, and where relativistic and retardation effects are omitted for simplicity; see Darwin Lagrangian.
The expression of the potential energy (3) suggests that it is a first part of a Taylor series, i.e. an approximation that is only sufficiently correct for small velocities and very low accelerations.
[17][18][19] The velocity-dependent term in the Weber force could cause a gas escaping from a container to become electrically charged.
However, because the electrons used to set these limits are Coulomb bound, renormalization effects may cancel the velocity-dependent corrections.
Other searches have spun current-carrying solenoids, observed metals as they cooled, and used superconductors to obtain a large drift velocity.
[21][22] Hermann von Helmholtz observed that Weber's electrodynamics predicts that charges in certain configurations can behave as if they had negative inertial mass.
[23] By measuring the oscillation frequency of a neon lamp inside a spherical conductor biased to a high voltage, this can be tested.
[15] Quantum electrodynamics (QED) is perhaps the most stringently tested theory in physics, with highly nontrivial predictions verified to an accuracy better than 10 parts per billion: See precision tests of QED.