Coulomb's Law and the Force Between Charged Bodies Across Vast Distances

[AeroKaro]

Homework Statement

We know that coulomb's law describes the force between two charged bodies as proportional to the magnitudes of the charges and inversely proportional to the square of the distance. Of course, like charges repel and unlike attract. Now theoretically, if we placed two opposite charges kilometers or even light-years apart, mathematically they would still feel an attractive force to each other. (Of course it is so minuscule, but still technically present.) As they start moving a tiny bit towards each other the force is greater because the distance is smaller. This increase in force would continue as they grew closer and closer together (since F(r)). Furthermore, if both were the same charge would they continue to repel each other indefinitely, even across monstrous distances like lightyears?

Homework Equations

The Attempt at a Solution

just plugging in values to r (no matter how large) there is still a force felt. Also in the vacuum of space, there would be nothing to oppose the force so Fnet would zero be zero?

 

[Orodruin]

mathematically they would still feel an attractive force to each other.

Yes, if the system is static. If the charges move, Coulomb's law is no longer completely accurate and you will need to turn to solving Maxwell's equations. Also note that if the charges start moving, it will take some time before the change in the field reaches faraway places. It cannot travel faster than light in vacuum.

 

[AeroKaro]

so Coulomb's law is strictly for charges that are held fixed in space, somehow. In other words it is not a good way of predicting the motion that the charges undertake

 

[SteamKing]

so Coulomb's law is strictly for charges that are held fixed in space, somehow. In other words it is not a good way of predicting the motion that the charges undertake

That's why there is electrostatics and electrodynamics; Coulomb versus Clerk Maxwell, Faraday, et al.

https://en.wikipedia.org/wiki/Electrostatics

https://en.wikipedia.org/wiki/Classical_electromagnetism

 

[Orodruin]

so Coulomb's law is strictly for charges that are held fixed in space, somehow. In other words it is not a good way of predicting the motion that the charges undertake

In some special cases, applying electrostatics to a dynamic situation will be sufficient, namely when velocities are low and the separations are so small that the speed of light is infinite for practical purposes. Otherwise you have to use Maxwell's equations.