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Here d denotes the exterior derivative – a natural coordinate- and metric-independent differential operator acting on forms, and the (dual) Hodge star operator is a linear transformation from the space of 2-forms to the space of (4 − 2)-forms defined by the metric in Minkowski space (in four dimensions even by any metric conformal to this ...
In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field , following the Biot–Savart law , and the other wire experiences a magnetic force as a consequence, following ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Kaufmann noticed that the observed increase cannot be explained by this formula, so he separated the measured total mass into a mechanical (true) mass and an electromagnetic (apparent) mass, the mechanical mass being considerably greater than the electromagnetic one.
The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles.
In the differential form formulation on arbitrary space times, F = 1 / 2 F αβ dx α ∧ dx β is the electromagnetic tensor considered as a 2-form, A = A α dx α is the potential 1-form, = is the current 3-form, d is the exterior derivative, and is the Hodge star on forms defined (up to its orientation, i.e. its sign) by the ...
The way in which charges and currents (i.e. streams of charges) interact with the electromagnetic field is described by Maxwell's equations [4] and the Lorentz force law. [5] Maxwell's equations detail how the electric field converges towards or diverges away from electric charges, how the magnetic field curls around electrical currents, and ...
It is therefore convenient to collect many of these terms in the Maxwell stress tensor, and to use tensor arithmetic to find the answer to the problem at hand. In the relativistic formulation of electromagnetism, the nine components of the Maxwell stress tensor appear, negated, as components of the electromagnetic stress–energy tensor , which ...