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The correct answer to this question is "Yes, it does", and it is one of the pitfalls concerning the application of Faraday's Law. For some people it is contraintuitive to assume that a Lorentz force is exerted to a charge although there is no relative motion between the magnet and the charge. [12]
But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions. Here, it takes the 2-form (F) and gives another 2-form (in four dimensions, n − p = 4 − 2 = 2).
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.
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.
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 ...
Analogously, Coulomb's law is the fundamental law that describes the force that charged objects exert on one another. It is given by the formula = where F is the force, k e is the Coulomb constant, q 1 and q 2 are the magnitudes of the two charges, and r 2 is the square of the distance between them. It describes the fact that like charges repel ...
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 ...
The force equation can be derived from the energy stored in a magnetic field. Energy is force times distance. Rearranging terms yields the equation above. The 1.6 T limit on the field [17] [19] mentioned above sets a limit on the maximum force per unit core area, or magnetic pressure, an iron-core electromagnet can exert; roughly: