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In inertial coordinates in special relativity, four-acceleration is defined as the rate of change in four-velocity with respect to the particle's proper time along its worldline. We can say: where. is the Lorentz factor for the speed (with ). A dot above a variable indicates a derivative with respect to the coordinate time in a given reference ...
Gravitational acceleration. In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag ). This is the steady gain in speed caused exclusively by gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the ...
In electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, [1] in the context of the wave theory of light . When any charged particle (such as an electron, a proton, or an ion) accelerates, energy is radiated in the form ...
Nonradiation condition. Classical nonradiation conditions define the conditions according to classical electromagnetism under which a distribution of accelerating charges will not emit electromagnetic radiation. According to the Larmor formula in classical electromagnetism, a single point charge under acceleration will emit electromagnetic ...
Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity.
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
The paradox of a charge in a gravitational field is an apparent physical paradox in the context of general relativity. A charged particle at rest in a gravitational field, such as on the surface of the Earth, must be supported by a force to prevent it from falling. According to the equivalence principle, it should be indistinguishable from a ...
In the standard inertial coordinates of special relativity, for unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time . In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four ...