Linear Superposition

## Question:

One property of electric force is 'a third charge will not
affect the forces exerted by 2 charges acting on each other'.
What is the assumption made in this property? Is it related to
something a force depends on?
I think of the size of the third charge. If the size is very
small, then the force between it and the 2 original charges will
be very small and thus not affecting them. But it seems wrong
because if the third charge is very small, what is the point of
adding the third charge?

## Answer:

The assumption underlying the assertion that a third charge does
not alter the interaction between the first two charges is the
assumption of "linear superposition". If linear
superposition is valid then you may find the effect of multiple
charges on a test charge by simply adding the effect of all the
charges on the test charge. There are some systems, for example
in some of the nuclear forces holding the nuclei of atoms
together, where this assumption is not valid but in the
interaction among electric charges, and the gravitational
interaction among bits of mass, it is true.
Remember that the assertion only says the third charge does
not change the interaction of the other two. Of course the third
charge does effect the interaction of the third charge with each
of the other two. In fact there are six effects to consider with
three charges, in three action-reaction pairs. The effect of
charge 1 on charge 2, the effect of charge 2 on charge 1 make up
one pair of effects. Likewise for the interactions between charge
1 and 3, and 2 and 3. The addition of charge 3 can not change the
interactions between 1 and 2.

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