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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