Let there be a system of $n$ source charges and a test charge $Q$. When we say superposition applies to electrostatic force, we conclude that the interaction between a given source charge and the test charge is independent of interaction between other source charges and the test charge. Why exactly it is the case? Also why some forces follow superposition?
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$\begingroup$ that's a postulation (that matches many observations). $\endgroup$– ShingCommented Feb 9, 2019 at 12:56
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2 Answers
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Superposition holds only because experiments show it to be true.
"Superposition is not a logical necessity, but an experimental fact" Source of quotation:- Introduction to Electrodynamics, David J Griffiths
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$\begingroup$ How/Why does superposition necessities the fact that the interaction between two charges is independent of third? $\endgroup$ Commented Feb 9, 2019 at 11:49
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Force is a vector quantity: vectors add in predictable ways, so forces are capable of being considered separately or of being added together.
We say 'superposition' if force fields (vector fields of a type OTHER than force) act on some part of an object, like mass or charge or surface area. An electric field, for instance, can make your (electrically polarizable) hair stand on end, while at the same time gravity makes your (massive) hair drape downward. Only a strong electric field overcomes gravity, but it never changes gravity. We observe this, but cannot say 'why'.
We can, however, calculate the electric and gravity forces and know how much electric field is required to balance gravity. The electric and gravity fields both generate forces, and we can sum those forces though the fields are as dissimilar as apples and oranges (and cannot be summed).
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$\begingroup$ Great idea. But gravitational and electric forces are different as you mentioned, they act on different particle, so one's effect on object (hairs) remain independent of the other. But in electrostatics we say that interaction between two charges is independent of third charge although there is some distortion in field lines between the two charges due to third charge. How then can we conclude? $\endgroup$ Commented Feb 9, 2019 at 22:53
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$\begingroup$ @user222267 Gravitational field is NOT force; only a mass in the field causes a force to come into existence. Electric field, in the presence of three charges, depends on all three, but the force on the third charge does not result from the field that third charge creates (that component of the field does not create a force on the third charge). By symmetry, it acts in no direction to create no directed force. $\endgroup$– Whit3rdCommented Feb 10, 2019 at 2:27