Francois Arago brought the news of Oersted’s discovery of the effect of a current-carrying wire on a magnet to Paris on September 4, 1820. André-Marie Ampère and the team of Jean-Baptiste Biot and Félix Savart quickly set to work to establish a quantitative law for this effect. Their approaches were quite different. This paper describes the experiments of Biot and Savart and their results. It also briefly discusses the approach of André-Marie Ampère, who coined the name “electrodynamics” and whose fundamental formula gave the force between two infinitesimal current elements. Ampere’s formula fell into disuse after the advent of Maxwell’s field approach. Biot and Savart’s experimental law, in the modern form of the differential magnetic field due to a current element, became the standard starting point for calculating the magnetic field due to steady currents.

Up to now, we have only considered stationary or static charges, which are sources of electrostatic fields. Stationary charges are studied in electrostatics. Electrokinetics, on the other hand, is the branch of electromagnetism devoted to the study of electric currents (i.e. moving charges) in a given medium, their evolution in time and their distribution in this medium. An electric current is therefore defined as a displacement of charge carriers. When electric charges are in motion, the expression for the electric field $\overrightarrow{\mathrm{E}}$ is modified. The electric currents produce not only an electric field but also a magnetic field that is manifested through a magnetic force exerted upon a charge in motion. An electric current can pass through a medium more or less easily, depending on the nature of this medium. This characteristic, called resistance, depends on the nature of the material and its temperature.

produce electric fields. A moving charge also produces a magnetic field. The interaction of electric charges with an electromagnetic field (a combination Electric charge (symbol q, sometimes Q) is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be positive or negative. Like charges repel each other and unlike charges attract each other. An object with no net charge is referred to as electrically neutral. Early knowledge of how charged substances interact is now called c Electric charge (symbol q, sometimes Q) is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be positive or negative. Like charges repel each other and unlike charges attract each other. An object with no net charge is referred to as electrically neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects. In an isolated system, the total charge stays the same - the amount of positive charge minus the amount of negative charge does not change over time. Electric charge carriers include subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a negative charge, if there are fewer it will have a positive charge, and if there are equal numbers it will be neutral. Charge is quantized: it…

In classical electrodynamics, the magnetic force is treated either as a fundamental interaction or as a relativistic byproduct of the electric field acting on moving charges. This paper explores a strictly kinematic and geometric interpretation of a magnetic-like interaction derived from the Concentric Shell Theory (CST). By modeling elementary particles as extended, stationary scalar wavefields, the transverse interaction—termed topological drag—between two such particles moving on parallel trajectories is numerically simulated. Integration of the interference energy demonstrates that Galilean rigid translation yields a constant force, failing to produce velocity-dependent transverse components. However, when the Lorentz spatial contraction is applied to the wave fronts of the moving particles, the geometric symmetry of the interference pattern breaks. The resulting differential transverse impulse is found to be numerically consistent with a v^2 scaling law, approximating the macroscopic behavior of the Lorentz magnetic force. A supplementary spatial analysis indicates a transverse decay proportional to d^{-1.30}, suggesting a possible long-range interaction envelope. This preliminary finding provides exploratory numerical evidence for a possible kinematic origin of velocity-dependent transverse interactions within the Concentric Shell Theory.

Physicists use the word field to describe the action of forces that one object exerts on other distant objects. For example, we say the Sun produces a gravitational field that controls Earth’s orbit, even though the Sun and Earth do not come directly into contact. Using this terminology, we can say that stationary electric charges produce electric fields, and moving electric charges also produce magnetic fields. Actually, the relationship between electric and magnetic phenomena is even more profound. Experiments showed that changing magnetic fields could produce electric currents (and thus changing electric fields), and changing electric currents could in turn produce changing magnetic fields. So once begun, electric and magnetic field changes could continue to trigger each other. Maxwell analyzed what would happen if electric charges were oscillating (moving constantly back and forth) and found that the resulting pattern of electric and magnetic fields would spread out and travel rapidly through space. Something similar happens when a raindrop strikes the surface of water or a frog jumps into a pond.

Lorentz force Lorentz's law is a law discovered by the Dutch physicist Hendrik Antoon Lorentz. Lorentz's law defines force that acts on moving charged particles in an electromagnetic field. Force consists of magnetic force and electric force. F = qE (electric force) If the charge is positive, the direction of the electric force is equal to direction of electric field. F = qv*B (magnetic force) The direction of the magnetic force is given by the right hand rule. If charged particles move with velocity v in an electric field E and a magnetic field B F = qE + qv*B F : force (vector) q : charge (scalar) E : electric field (vector) v : velocity of particle (vector) B : magnetic field (vector) * is vector cross product. Using this law, J.J. Thomson measured mass-to-charge ratio.

The Forces Acting on a Charged Condenser moving through Space ← The Forces Acting on a Charged Condenser moving through Space ( 1903 ) Frederick Thomas Trouton and H. R. Noble → related portals : Relativity sister projects : Wikipedia article , Wikidata item Proceedings Royal Society London 74 (479): 132-133 Online 648278 The Forces Acting on a Charged Condenser moving through Space 1903 Frederick Thomas Trouton and H. R. Noble " The Forces Acting on a Charged Condenser moving through Space. " By Professor F. T. Trouton , F.R.S., and H. R. Noble , B.Sc., University College, London. Received June 11, — Read June 18, 1903. (Abstract.) If a charged condenser be placed with its plane in the direction of the æther drift, then on the assumption that a moving charge develops a magnetic field, there will be associated with the condenser a magnetic field perpendicular to the lines of electric induction, and to the direction of the motion. If N be the electrostatic energy of the condenser, the magnetic energy produced when moving with velocity w through the æther with its plates parallel to the motion is N( w/v )², where v is the usual velocity of propagation. But when the plates of the condenser are perpendicular to the direction of motion, the effects of the opposite charges will neutralise each other, and there will be no magnetic field produced. Thus if we have a condenser freely suspended with its plates making an angle ψ with the direction of the æther drift, the magnetic energy

Electromagnetic effects of a moving charge ← Electromagnetic waves, the propagation of potential, and the electromagnetic effects of a moving charge ( 1888 ) by Oliver Heaviside → related portals : Relativity sister projects : Wikidata item Electrical papers, 1894, vol. 2, pp. 490-499, Online [ The Electrician : Part I, Nov. 9, 1888, p. 23; Part II, Nov. 23, 1888, p. 83; Part III, Dec. 7, 1888, p. 147; Part IV, Sept. 6, 1889, p. 458.] 420795 Electromagnetic waves, the propagation of potential, and the electromagnetic effects of a moving charge 1888 Oliver Heaviside ​ PART I. IN connection with the letters of Profs. Poynting and Lodge in The Electrician , Nov. 2, 1888, I believe that the following extract from a letter from Sir William Thomson (which I have permission to publish) will be of interest [see Postscript, p. 483, vol. II., to elucidate]: "I don't agree that velocity of propagation of electric potential is a merely metaphysical question. Consider an electrified globe, A, moved to and fro, with simple harmonic motion, if you please, to fix the ideas. Consider very quickly-acting electroscopes B, B', at different distances from A. If the indications of B, B' were exactly in the same phase, however their places are changed, the velocity of propagation of electric potential would be infinite; but if they showed differences of phase, they would demonstrate a velocity of propagation of electric potential. "Neither is velocity of propagation of 'vector-potential' metaphysic