Retarded And Advanced Potential
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Retarded And Advanced Potential
In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light ''c'', so the delay of the fields connecting cause and effect at earlier and later times is an important factor: the signal takes a finite time to propagate from a point in the charge or current distribution (the point of cause) to another point in space (where the effect is measured), see figure below. In the Lorenz gauge The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: : \Box \varphi = \dfrac \,,\quad \Box \mathbf = \mu_0\mathbf where φ(r, ''t'') is the electric potential and A(r, ''t'') is the magnetic vector potential, for an arbitrary source of charge density ρ(r, ''t'') and current density J(r, ''t''), and \Box is the D'Alembert operator. Solving these gives the retarded potentials below ...
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Electrodynamics
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electricity and magnetism, two distinct but closely intertwined phenomena. In essence, electric forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between ''moving'' charged particles. These two effects combine to create electromagnetic fields in the vicinity of charge particles, which can exert influence on other particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force. The electromagnetic force is responsible for many o ...
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