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Say you have a positive electric charge at point A in empty space. Across ten light years there is another positive charge at point B.

The charge at point B has forces on it from the charge at point A. If the charge at point A was changed to a negative one, does the direction of force on charge B change instantly? Additionally, is there any limit to the distance at which these forces can be produced?

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Changes like that are propagated through space at the speed of light, as electromagnetic waves. There is no limit to their range.

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According to the classical theory of electromagnetism, there is no limit. The force has an infinite range. This would not be true if the photon were not massless. There have been many experiments measuring the photon mass, and we can say with certainty it is less than $10^{-18}~eV/c^2$

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While there is not technically a limit, fundamental forces have a pretty steep falloff. As your distance increases, the strength of the field decreases proportional to the square of the distance.

Now, while this technically means that every single electron in Proxima Centauri influences the simple electromagnet from test question 4.b, because of the distance between the star and us (roughly 3LY, if I recall correctly) the force felt from it is so minuscule as to be unsubstantial in the scope of your equation.

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