Sunday 17 July 2016

newtonian mechanics - How do varying static point charges exert the same force on each other?



If you have two point charges one being 1 Coulomb and the other being 1 Trillion Coulomb, it is said that the electric force from the 1 Coulomb point charge exerted on the 1 trillion Coulomb point charge is equivalent to the electric force from the 1 trillion coulomb point charge exerted on the 1 Coulomb point charge.


How can a 1 coulomb point charge exert the same force as a 1 trillion coulomb point charge?



Answer



Perhaps this analogy will help:


Imagine I have two fans - one with a huge diameter, the other with a tiny diameter. When I put them facing each other, with the huge fan running, I will be able to extract a small amount of power from the tiny fan (because only a tiny fraction of the wind generated by the big fan will intersect with it). Conversely, when the tiny fan is running, almost all its air will be "felt" by the huge fan. But the tiny fan only generates a little bit of air movement...


This is how it is with two different charges (or if you like with two different masses). The same thing (charge, mass) that makes them able to generate a field, makes them susceptible to the field of another (charge, mass). This is indeed a necessary consequence of Newton's third law - the attractive force must be reciprocal (force of A on B must equal force of B on A), so there must be symmetry in the equation describing the force.


If you are OK with the force of Moon on Earth being the same as the force of Earth on Moon, then you should be OK with this. And if those forces were not the same, their would either be crashing into each other, or flying apart...


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